So I've set the cycles in DOSBox to a speed that feels comfortable not too fast and not too slow. However the battles always seem to run at a different speed. The AI units are just crazy fast and I can barely track where they're going. Is there some kind of setting or solution for this? Atm I'll just have to manually change the speed whenever I'm in a battle and change back afterwards.

I don't recall if it's the case for Pool of Radiance, but some of the games have a speed setting you can access from the Encamp menu. It's "Encamp -> Alter -> Speed" in some of the games.

There tends to be two speed settings.
The encamp menu one is generally text speed
The second is the 'speed' option in combat, which changes combat speed (often defaulted to the fastest).

Try the combat option, 3 is 'normal' speed the game, but play with it till you fine the one that best suits you.