RX continues to be my Swiss army knife for this sort of thing. You need at least the Standard version to have Spectral Repair. It takes a lot of practice and experimentation, but I've gotten some amazing results with it.
The greatest magic trick I ever pulled off with it was this past May. I was working on a classical choir and chamber orchestra concert, where the first violinist had a persistent and very loud cough all through the 40-minute piece being performed. Guess where the main mic array was located? And did she avoid coughing in the quiet sections? I was able to reduce the 100+ loud coughs to the point where most were completely inaudible, but it took a lot of work. Not all the coughs were processed the same way, either. Some used Attenuate; others Replace. Oh, and the organist hit a chord very fast but a measure early. I was able to zap that as well. Basically RX enabled me to take a recording with lots of distractions and make it quite nice to listen to.
Now, I'm not saying it will cure your situation for sure, but it's your best bet, IMO. I'd be happy to take a crack at it over the weekend if you send a sample.