I had my recording levels too high at this event I captured and I plan to replace a lot of the audio with music, but is there anything I can do to fix the distortion on areas like dialogue that I want to keep in post?
Not really. Is one channel better than the other? If so, you could bring it into an audio fixing suite like soundsoap and try massaging it. It is likely too far gone.
Your could ADR the dialogue parts.
Best bet is to always bring one channel down -10db. That way if any parts clip you can replace it with the good channel.
Well actually RX by iZotope can do some amazing things to blown out audio. It really depends on how much is hiding in the distortion, sometimes there is nothing left but sometimes there is a lot.