This is an interesting thread which raises lots of tricky issues with
good suggestions from all previous posters.
I think the main thing here is to be realistic about what sound quality youre looking for over the entire project, and more importantly what your clients expectations are. Having multiple microphones open all the time, and with so many variables, I think without constant mixing supervision, the results will be at best average. Adequate depends on those expectations.
It may be that achieving a higher quality sound track will require will require a completely different level of attention throughout, and therefore budget. No doubt your client wont like that, but it might be the truth.
Have you ruled out wired personal mics on everybody, with a computer based multitrack recording individual streams locked to tc from the camera. ?
Peter