Thanks much for your thoughts here. I think the period between South Mountain and the attacks of the 17th is the most fascinating tactical situation of the war. You make commendable points. I don't think we're far apart on the general idea. Perhaps two corps couldn't be over the creek by noon. I bet bolder generals might have found a way, especially since we are talking 36 full hours since South Mountain on the morning of the 16th (even after the fog). I don't think McC was looking for a major battle after South Mountain. Carman has good points on that subject.
In the first place, it's pretty much a rule of thumb that only 30,000 men can fit down a road in a day. So one full day's worth of that time would be consumed in just
getting the troops over South Mountain under normal operations - there was a truly massive traffic jam - then it's about 5-6 miles, or the majority of a day's march, from the South Mountain gaps to Keedysville.
I can certainly buy the idea that a well coordinated army would have done better, but McClellan wasn't using a well coordinated army. He'd had only about a week to organize it before leaving Washington and some of the details were still being thrown together on the march.
As for the idea McClellan wasn't looking for a major battle after South Mountain, if that were true he could have just thrown 1st and 12th Corps across the creek and held them in position around Smoketown and Mercersville. Instead, he attacked; he was willing to take the battle on the 17th, and indeed make an attempt at a battle of annihalation (and ended up producing a battle of attrition in his favour).
I'm not in total agreement on your analysis of McC's defense of his decision on the 18th. He felt without absolute certainty, he would not attack due to the circumstances. He certainly mentioned the risk involved, but he also wrote of his "narrow view of the condition of the country" and another battle needed "absolute assurance" of the best outcome. Again, he wished for something no army commander could ask in war at a time when Lee's own battered troops had a river with one ford at their back. Any "narrow view of the condition of the country" from the other general's perspective makes McC look a bit over cautious. If Lee had 120K men along the Antietam, as McC suggested he did, why attack at all? One corps across the creek against 120K Confederates?
This simply doesn't hold. McClellan's in a situation where he has basically no spare troops to attack with on the 18th, and what that means is that if he attacks anyway and is defeated then Lee can
counterattack and wreck his army; the Union has suffered several defeats in a row which have caused panic, and can't endure another.
(That's what the "condition of the country" means.)
McClellan's attacks on the 17th don't risk his army, because he always has enough troops in hand to recover the situation if the attack fails. An attack on the 18th
would risk his army, because it'd be using his last reserves, or if he didn't overcommit it would be too small an attack to have any effect (a couple of brigades).
As for the size of Lee's army, I suspect that McClellan thought Lee might have had 120,000 Aggregate Present at the most (which is an army about the same size as McClellan's own on the field). This is an estimate which has at least some reasoning behind it, and is basically flawed because the Union reconstruction of the Confederate ORBAT is flawed (they missed the brigades left behind to defend Richmond).
McClellan's actions make sense if he thought that Lee's army was close in size to his own.
You are right that clear orders would not have guaranteed a better outcome. Yet, I have seen no pre-battle written attack plan regarding McC's goal for the 17th. I've never seen a source showing there was a council of war before the battle. McC changed his story after the war. I have no problem with those critical of Hooker on the 16th or 17th, but McC does not deserve a pass (and I'm not saying you are giving him one).
My understanding is that 12th Corps were ordered over the creek on the 16th, and basically that they began crossing as soon as 1st Corps finished crossing the bridge; this may be wrong, of course. 2nd Corps pulls in to support the possibility of an attack over the middle bridge, so as the corps arrive it's:
1st Corps (arrives first) - goes to upper bridge (as that's where McClellan needs troops then)
2nd Corps (arrives second) - goes to middle bridge (so there's troops to support an attack there if needed)
12th Corps (arrives third) - goes to upper bridge (to bulk out the flank attack)
Then 2nd Corps is diverted to the upper bridge later on. Richardson's Division isn't sent until McClellan has another division to make up his central reserve in their place (Morell).
The coordination is messed up because it's an army with officers that haven't worked together and some that have never held high command before. The exegiencies of how Burnside's wing got split up after South Mountain and the way that corps are being moved around according to which is in the best physical location to do what's needed mean the command structure gets scrambled.
i.e. Hooker (who is the first officer over the creek) is new to corps command, and is doing okay considering but hasn't yet got into the habit of coordinating
someone else's corps as well as his own.
Mansfield (commanding 12th Corps) is new to corps command also, and stuffs it up acting like a junior officer.
Sumner (commanding 2nd Corps) is
not new to corps command, but goes to the wrong place and doesn't find McClellan for a discussion overnight; he's also been working hard keeping his wing going in the right direction, because at one point 12th Corps turned north at Boonsboro and had to be redirected.
Under the circumstances, it's if anything surprising the attack in the north did so well; certainly getting 45,000 men PFD attacking on the same axis in a single day is one of the largest attacks of its type in the war.