As for "what Porter could have done better at Second Bull Run", you seem like a pretty sharp guy so I'll let you take a crack at it first before giving the answer. There is one but let's see what you come up with. You should start with August 28 late and work forward. And feel free to take the full 49 weeks if needed, which appears to be the default time frame for responding in this Porter sub-thread.
I'll admit I was rather hoping your work wasn't getting in the way any more.
Let's see...
28th
Porter marches from Warrenton Junction at 3AM and arrives at Bristoe Station 10:30 AM, remains there for the rest of the day
I can't find a mention of Porter being ordered to the battlefield on the 28th in Hennessy; Hennesey lists orders to King, McDowell, Kearny, Heintzeman, Reno and Sigel, but none to Porter. If Pope forgot to send Porter orders then that's on him; if Pope thought McDowell would pass on orders then that's also a mistake.
I assume what you're thinking of is that he should have marched to the sound of the guns in the afternoon, but no such charge is in the accusations of which he was convicted in the court-martial. There is an accusation that he started marching to Bristoe at 3AM instead of 1AM, but that's nothing remarkable and he was acquitted in the Schofield report on the grounds that he still got moving at a reasonable time. He marched about 10 miles (from modern Calverton to Bristoe Station) which is a serviceable day's march.
29th
3AM August 29th Porter is ordered to move on Centreville at dawn.
Just after dawn Pope moves to Centreville himself, and upon arrival sends orders via McDowell to turn King's division over to Porter and have Porter and King march to Gainesville (delivered by Piatt, who apparently failed to make clear that Piatt's brigade was now attached to Porter).
The final set of orders on the morning of the 29th to Porter reach him at Manassas at 9:30 (delivered by Gibbon), and is to push 5th Corps plus King's division to Gainesville.
Piatt was under Porter's command, but apparently Porter was unaware of that fact until 16 years after the battle.
10AM to noon
The Joint Order is issued. It contains these elements:
- Move to Gainesville.
- "The whole command shall halt" as soon as communication is established between the main body and the combined 1st/5th Corps wing.
- order not to be strictly carried out if advantage can be gained by departing from it.
- troops must occupy a position from which they can reach Bull Run by tomorrow morning (as they may need to fall back behind the river tonight).
Porter is on the march up the road parallel to the Manassas Gap railroad, which is the correct road to take to get most directly to Gainesville, as is McDowell behind him. The combined force (under McDowell's command as senior general) runs into enemy troops and halts; McDowell decides to take the Sudley Springs road (to the right of the Gainesville road) and have Porter stay where he is.
The Porter retrial concluded that Porter had complied with the order as much as possible, as it had essentially run into Longstreet, and that to expect Porter to somehow punch through Longstreet was too much (while having Porter keep Longstreet in check and be ready to fall back behind Bull Run that night was doable and was what he did).
Noon to 2PM
Pope writes of this period that he expected Porter and McDowell were moving to Gainesville and were going to outflank and turn the enemy; in fact they'd run into elements of Longstreet's "corps" and thus were unable to do so.
Porter remains basically engaged to his front and tries movements to the right, but doesn't hit on a solution.
2-4 PM
Porter assumes a defensive posture, in accord with McDowell's opinion.
He does not fall back despite the opinion of Morell (for the rest of the day; it's in his orders in the ORs.)
4-6 PM
4:30 - Pope writes an order to Porter to attack the enemy flank and if possible rear. (Porter is actually aimed at Longstreet's entire corps.) This order will not arrive until around dusk.
Porter considers falling back but decides against it; he also considers an attack, but decides against it because the enemy is still in his front. Griffin's brigade withdraws but this does not seem to have resulted from Porter's orders.
Around 6PM Porter checks with McDowell what he should be doing.
6PM-midnight
Pope believes Jackson is retreating.
Pope is now aware that Longstreet has arrived, but believes Longstreet has not extended Jackson's line; he thus believes that Jackson's right is still vulnerable to an attack by Porter moving towards Gainesville. (This is an incorrect belief on Pope's part.)
When Porter's 6PM dispatch is mentioned, Pope is unaware that the 4:30 order to attack had not been recieved; he thought Porter's actions were disloyal, but McDowell said it was the result of incompetence.
Pope sends an order to Porter directing him to "march his command to the field of battle of today and report to me in person for orders". This order is peremptory.
Porter orders an advance around 6PM based on information that the enemy is retreating, and then recieves the 4:30 PM attack order. He orders an attack, but Morell protests that the enemy is not retreating, and since it's now basically dusk Morell's opinion that an attack would be a bad idea is followed.
So basically the 5th Corps skirmishes all day. It might be possible to argue that Porter should have pushed more aggressively to his front, but given that
(1) his orders of the morning included a directive to be able to retreat behind the Bull Run overnight
(2) he was in fact facing a grind through Longstreet's entire corps if he'd continued to advance
(3) McDowell, his senior, had modified the "move on Gainesville" orders by removing more than half of the strength of the column tasked to carry them out, leaving Porter with just two divisions instead of the five initially tasked
(4) McDowell had also said it'd be better if Porter held his position
I think you can argue that the decision was the correct one with hindsight; you can also argue that given what Porter could know at the time it was the correct decision.
The inital court-martial had as a basis that Longstreet was not present; the retrial noted that he was. Similarly the initial court-martial got Porter's position wrong.
To summarize the findings of the retrial on these respects, it would be that the initial court-martial had Porter close enough to fall on Jackson's right and also had Longstreet not present; both of these were entirely false.
I'm not really seeing it, I'm afraid, or rather I can see
an alternative (which is to continue the advance to Gainesville with a set-piece attack past Dawkins' Branch) but this would in fact have just led to Porter running straight into Longstreet's whole corps with his own much weaker force.