Your screenshots are helpful, though of course it's hard to know everything that has been going on. I do note that you don't seem to have tried any amphibious invasions. That would hurt the CSA in one way, but at the same time it would be facing fewer forces up north. So that's an issue, though not the main one.
I gave him a ton of resources. If he won't build brigades, I'm not sure what to tell you. As for how many brigades I've captured, I never have captured more than two at a time, but he loses a lot of brigades by attacking my western armies with divisions and then retreating. Still, I'd be surprised if it totaled more than 10 the entire game, considering how often I reload when CSA brigades surrender.
What do you mean by "a ton" of resources? Is this still 1st Sgt., or did you try a higher level?
Higher up in the thread you wrote:
I didn't think it was just a CSA problem. It's a capital bias problem. The AI overvalues the capital province (when this discussion first began in another thread, Gil even said it was something they were looking at tweaking; he's backed off that now). It's a pretty obvious problem to see, when you create the conditions that cause it. A lot of players play too high of a difficulty level or deliberately play a strategy that avoids causing the migration (HS mentioned in his test AAR in the main forum that he doesn't muster much), but I'm pretty sure you can make it happen on any difficulty level.
I have not backed off that statement. You must have misread something I wrote. As you'll see below, I still believe that the CSA AI can sometimes hurt its overall strategy by overemphasizing the defense of Richmond, but even though we have yet to see proof that this is a serious problem affecting multiple players we are considering ways to make that less pronounced.
Much as you hate AI bonuses, why don't you play a game or two on one of the 2-3 highest levels and use your approach and see if this really does happen? That would provide more useful data points that playing multiple games at 1st Sgt. or a comparably low level.
The thing to understand about the CSA AI is that it is programmed to fight defensively most of the time (with occasional bursts of aggressiveness, like Lee's heading into Union territory twice, in order to keep the Union player from becoming complacent). This means that if the CSA AI expects to lose, it usually will not engage. What's happening in your games is two things: out west the AI sees it's going to lose, and back in Richmond there is a perceived threat, so those western armies head to the eastern theater rather than be destroyed.
The graph you posted showing strength is a bit instructive, but doesn't tell us the whole picture. The AI judges its odds not just based on the respective sizes of the armies, but also weapons and brigade attributes -- both of which require resources. (I've been referring only to troop strength, and should have noted this earlier. I forgot that the AI includes those in its calculations as well.) If you play at one of the easiest levels then not only does the AI produce fewer troops, it does not arm them as well as the North (which already has a massive advantage in iron, money, and weaponry), and also can't purchase as many brigade attributes. (There's another graph for weapons, though not brigade attributes -- perhaps check that and see how things look.)
And here's a related issue: if we increase the CSA AI's aggressiveness, then we will be hearing an awful lot of complaints from players who see the CSA making suicidal attacks that destroy its armies. The CSA is at a manpower and resources disadvantage, so the CSA AI
can't be programmed to become more aggressive, since that guarantees it will lose routinely at all but the very highest difficulty levels. (It might survive longer by bloodying the Union a bit more, but ultimately it will destroy itself. So instead of falling back to Richmond in 1863 you'd see its armies decimated over and over until they evaporate in 1863 or 1864.)
As I've said before, I understand your position on not wanting to play a game in which the AI has bonuses, but as I've pointed out before, computer games typically do have such bonuses. As you know, the way companies make AI's tougher is by AI cheats and AI resource bonuses (since the notion that one should program an AI to be "smarter" at higher levels is preposterous), and we've taken the bonuses route with FOF. The most fundamental thing to know about playing any computer game is that if you are beating it at an easy level then you increase the difficulty, but you're not doing this. I guarantee you that at higher difficulty levels what you're complaining about will not happen nearly as much. And as I've noted previously, the game was balanced and tested for typical players, i.e. those with no compunction about playing an increasingly wealthier AI.
Does any of that mean that I'm going back on my earlier statement that the high value placed on Richmond can create a problem for the AI? No. But I do not believe it is as big a problem as you are making it out to be. As I have already said, we will consider what might be done to make this less common at lower levels next time we produce a FOF patch, since obviously we want the game to be challenging at all levels. (Our programmer has suggested that maybe he can have the AI not bother with Richmond at the lowest 2-3 levels -- a change that would be relatively easy for him to make, and that might be worth testing when the time comes.) But we don't feel that the product is flawed if it can be easily beaten at a low difficulty level. And until it is proven that the CSA AI collapses and hightails it to Richmond at higher difficulty levels and when faced by a Union opponent using a normal strategy (which includes thinning out its armies by sending some forces by sea to the eastern and southern coastlines) we will have no reason to conclude that this is a serious AI flaw.
(though if you're like most here, you don't play the balanced difficulty levels). I seldom deviate from a set plan and my games always produce the same result. In general though, I think the key is to pack two army containers in the east to max size. I usually am able to eventually push them into Fredericksburg and Rappahannock (behind fortresses), but I really don't think it matters. He'll migrate east even if you just sit in D.C. and Maryland (see the last two screenshots above for January 1863 and then May 1863). 
