Saphroneth, the answers to your Alexander's Bridge questions in posts #506, #508 and earlier are largely answered by the Confederate reports, principally Walthall's, Smith's, Campbell's, Brantly's, Johnson's, Benton's and Liddell's, as you may already be aware. All quotes are from O.R. series I, vol. 30, part II.
Low casualties in the 24th and 27th, the two regiments on the right, are explained by their having largely missed the fight:
Brig. Gen. Walthall reports: "the two regiments on the right [24th MS and 27th MS] meeting no opposition, except in front of the two companies on the left of the Twenty-seventh Regiment." {i.e., only the two companies nearest the hard-hit 29th} (Oct. 6, p. 272.) Why did they miss the fight? Because they became thoroughly disrupted by being on the outside of a left wheel in dense woods:
Capt. Smith, 24th reports: "The movement of the regiments on our left being being very rapid, and the direction of the front of the brigade being changed to the left the 24th, soon after starting, was compelled, in order to keep upon the line, to take the double-quick and then the run, making something similar to a 'left wheel', which continued for nearly a mile. In this movement the regiment became much confused and scattered, and did not arrive on the line at the river in time to take any part in the engagement which occurred there, any more than to fire a few shots at the enemy's skirmishers." (Smith, Senior Captain, Commanding, 24th MS, No Date, p. 277.)
Col. Campbell, 27th MS reports: "The forward movement commenced, but owing to the fact that the woods were very dense and many fences to cross, and that the regiments on the right of the brigade (my regiment being next to the right regiment) had much farther to march than those on the left, the movement assumed more the nature of a left wheel than a forward movement, and my regiment was compelled to take the double-quick step, which caused some confusion, but pressed forward as fast as possible until my left struck the bank of the creek, at which point the enemy from the other side of the creek fired upon them, which was responded to promptly and sharply. On discovering that the banks of the creek were very abrupt on both sides, and not knowing the depth of the water, I ordered my regiment to lie down on the bank of the creek and hold their position. The enemy abandoned his position...." (Oct. 5, p. 279.)
Where did the 29th suffer its heavy casualties and who caused them? In the center, at the bridge, and caused by the Spencer-armed infantry on the opposite bank. Much of this was already covered in post #429 but here goes again.
Walthall reports: "I moved forward through a dense thicket, and after advancing a quarter of a mile the enemy's skirmishers were encountered in front of my left and center.....The road on which my left rested in the beginning of the movement turns to the right at a point 200 or 300 yards from the bridge, forming a right angle. At this point the [34th MS and 30th MS], in advancing passed across the road into an open field, and the Twenty-ninth Mississippi Regiment, Colonel Brantley (the center regiment), being immediately opposite the bridge was stubbornly resisted for about fifteen minutes, and in the meantime the regiments to the left of this, driving the skirmishers of the enemy before them, swung round under the enemy's artillery fire through an open field until the line they formed was nearly at right angles to that formed by the other three regiments, conforming in the main to the general direction of the creek. When the bridge was gained by the 29th Mississippi Regiment it was done under a heavy fire from the enemy posted on the opposite bank of the creek....In this action the Twenty-ninth Mississippi Regiment lost heavily...." (Oct. 6, pp. 271-72)
Col. Brantly reports: "My regiment struck the enemy in considerable force near and immediately in front of the bridge above mentioned, and a fierce engagement ensued. I pressed forward with my command and took possession of the bridge, which had been so torn up as to prevent crossing. In this engagement the loss of my regiment was 56 killed and wounded." (Oct. 5, p. 282)
Col. Govan reports: "Walthall's brigade, moving forward, soon engaged the enemy, who occupied a dense thicket on the south side of the creek, near the bridge. After firing several volleys he retreated, leaving us in possession of the bridge, which was, however, rendered useless, the planks having been removed. The brigade was not actively engaged excepting the skirmishers, who were thrown forward on General Walthall's left to the creek, sustaining a loss of 1 killed and 5 wounded." (Col. Govan, commanding Liddell's brigade, Oct. 6, p. 257) [Govan's skirmishers (one or two companies per regiment) engaged Wilder's skirmishers on the Confederate left and perhaps across the creek with the Co. F, 72d Indiana which was on the left (from the Confederate perspective) (upstream) of Co. A, 72d in the lunette. The company from 8th Arkansas "had three men slightly wounded by the shells of the enemy" (p. 268). The 5th Arkansas threw out two companies as skirmishers, who engaged Union skirmishers on the south side of the creek. "The regiment was in the meantime also moved forward...but, though subjected to a heavy fire of artillery, which wounded 2 men ... did not become engaged." (pp. 262-63).]
Capt. Swett, Acting Chief of Artillery, reports: "The enemy had but one battery, which was posted near a house on the opposite bank. of the creek, and which fired upon our skirmishers, a few shots passing over the line. Fowler's battery was moved to the front and placed in position near the road and on the edge of a cultivated field....
Brig Gen. Liddell reports: "I instructed Brigadier-General Walthall, of my division, to make an attack upon the enemy in possession of the bridge....The force in our front consisted of Wilder's mounted infantry, from which were captured a half-dozen or more breechloading rifles. Our loss was 105 in killed and wounded, and I can only account for this disproportion from the efficiency of this new weapon, our attack having been made through thick woods an cedar underbrush, rendering the artillery of the enemy that was used on the occasion relatively harmless."
Why the moderate casualties in the 34th (25) and only slight in the 30th? The 34th engaged Wilder's "main line" at relatively close range; the 30th spent most of the battle behind a hill.
As mentioned above, The road (on which Walthall's left flank rested) "turns to the right at a point 200 or 300 yards from the bridge, forming a right angle. At this point the [34th MS and 30th MS], in advancing passed across the road into an open field," and while the 29th was engaged in its firefight with the defenders of the bridge, "the regiments to the left of this, driving the skirmishers of the enemy before them, swung round under the enemy's artillery fire through an open field until the line they formed was nearly at right angles to that formed by the other three regiments, conforming in the main to the general direction of the creek." (Walthall, p. 272)
Maj. Johnson, 30th MS reports: "When the signal to advance was sounded the regiment moved forward, guiding left, and after advancing about half a mile we crossed the road which led to the bridge. This road her made an abrupt turn to the right, forming a complete right angle. The regiment advance some 300 or 400 yards through an open field under the fire of the enemy, who were posted on a hill immediately in our front. [these are likely federal skirmishers on the hill Johnson's skirmishers eventually briefly occupy] Here it was found that this regiment, with the 34th (the regiment on our immediate left), had become separated from the balance of the brigade, and the order was given to the men to lie down behind an abrupt hill in the field. Here Colonel Scales ordered the men to cease firing (the enemy having disappeared)[likely means the federal skirmishers have finally left and crossed the creek] and dispatched the adjutant to the brigadier-general to report the position and the situation of the regiment. The brigadier-general arriving on the ground[all of this takes time], ordered the colonel to press forward his skirmishers and occupy the hill, which was done. The skirmishers had hardly occupied the hill when the brigadier-general ordered them to be withdrawn, and the regiment to move back and join the balance of the brigade," which then marched to Byram's Ford. (Oct. 5, pp. 282-83) Thus, the 30th appears to have been under skirmisher fire for several hundred yards and then spent much of the action behind an abrupt hill, hence its slight casualties (5 wounded). It may possibly also have been under ineffective long range artillery fire though there is no mention of it in the regiment's report.
Col. Benton, 34th MS reports: "A company of skirmishers had been thrown forward, but as the line was not parallel to the stream, owing to wrong information as to the roads, the brigade had to swing rapidly around to the right, and it was difficult for the skirmishers to keep in advance. The command moved across an old field, in which the enemy's skirmishers were encountered and driven back. Advancing toward the stream at a point above the bridge [i.e., to the left, not the right, of the bridge], a destructive fire was received from the enemy's main line, under cover of a skirt of timber and dense undergrowth [is this perhaps Co. F, 72d, or cross-fire on Co. A, 72d?]. It was promptly returned and after a sharp engagement of twenty to thirty minutes they were dislodged from their position. The bridge having been destroyed by the enemy, the regiment moved with the brigade a mile a half further down to Byram's ford and crossed....The command behaved with steadiness and spirit, and sustained a loss of 24 wounded, 2 of whom died shortly afterward. The wounds of several of the others were severe. " (Oct. 6, pp. 284-85)
Thus, the two regiments (29th and 34th) who engaged closely with Wilder's "main line" suffered severely. The other three regiments, two of whom missed the fight almost entirely and one which spent most of it sheltered behind an abrupt hill after passing several hundred yards either under skirmisher fire or long range artillery fire, did not. Few casualties were credited to artillery fire.
Bragg's map in the O.R. Atlas shows the Confederates hitting the bridge straight on and on both sides of it, consistent with the above descriptions by Brantly and Benton, but it is not a very detailed map.