I'm in a similar situation, I can beat the AI on any difficulty, as both sides. The only real thing I find I need to worry about is cycling troops on and off the front line, so I can always keep pushing. The confederates have the numerical superiority on the first day, so as long as you keep about 1/4 of your troops in reserve it isn't a problem.
The reason the AI struggles here is that it does no unit cycling. The same units will sit on the front line until they rout, at which point they're effectively out of combat for several in-game hours. Whereas my cycled troops, once they get to ~20% condition, are replaced by a full condition and morale brigade, while the replaced unit can withdraw and rest. The other useful tactic is to keep a large brigade in reserve, and once your front lines have engaged for some time, charge the large brigade into their lines. This often causes mass routs, and even if it doesn't it means your troops can still shoot into the melee, while their troops are all tied up in melee, resulting in them receiving massive casualties.
What I've found myself doing is attempting to unlock all the scenarios, by either attacking and taking only one or two key points, or as defenders deliberately abandoning points. It leads to some much more interesting fights, often where Confederates have to attack Union forces that are 30% larger than itself.