Could a shotgun mic placed (perhaps several feet away and concealed) be employed here, pointing it in the general direction of the activity to be recorded? It would at least to some extent filter out the room sound. I've seen them employed for interviews on talk shows several feet from the subject in place of a lavlier when the subject's clothes did not lend itself to miking up the subject directly and the resulting audio seemed almost as good as close mike techniques.

Stu