So I get to the fight with the three waves and the kobold king, but the game ALWAYS crashes during the third wave. I'm using goldbox companion, but I've read that this has always been something that could happen. Is there any way around it?

I have some vague recollection that the crashes are tied to the boars and their ability to rise up again after being defeated.
You may want to try using a DOSBox version with Save States function; then you don't need to fight the first two battles over and over again.