Hello LostDaimyo!

You've already stated the most obvious solution. If you've scouted the enemy army then you can easily prepare for the encounter by bringing an army comp that best counters the opposing army comp. This isn't a perfect solution though because the A.I. makes it's moves after the player. This means that the army you've scouted can change it's comp during the end turn and thereby ruining your perfect plan. I prefer to bring balanced armies in my campaigns, then I'll just adapt to each situation as it happens.

For starters I always play with the battle timer on. This means that when I'm on defense I can simply let the enemy come to me. If the A.I. doesn't want to charge it's six CA's into my spear wall that's sitting inside a forest on top of a hill then that's fine by me, I'll simply time them out for a win.

Things can get a little tricky though on offence. In the situation where you've described where the enemy has a ton of reinforcements and I'm the attacker I'm already going into the battle knowing that I'll lose the first one just because I'll get timed out. There simply won't be enough time on the game clock to beat multiple waves of reinforcements. I can beat two, three, maybe even four if the map is small but eventually I'll get timed out. That's okay, I'll simply attack again during the next turn. "Losing" battles in this way is okay as long as the kill ratio is in your favor and/or you have a strong economy.

This means that those annoying "pests" of CA will get slowly whittled down over the course of two, three or four battles. They'll come into range of my archers, I'll shoot them until I run out of arrows or they run away. Maybe I kill a general, maybe I don't. It doesn't matter. As long as I'm playing with the game timer on these problems rarely become actual issues.

If I do actually need to chase down a unit or two that won't engage with my "victorious" force then I'll simply keep my formation wide, spread my lines thin and cast a wide net using a center group and a left flank and a right flank to corner a kill/route off any leftovers.

If you think that playing with the game timer on is cheap or unrealistic then just keep in mind that armies in real life typically don't fight at night time ! I think of the game timer as a day clock. The bottom line is that the reinforcement system in this game is pretty crappy and being forced to attack when you're the defender but the A.I. refuses to attack you is also crappy. So avoid the crappy parts of the game I say! I hope this has helped