A lot of non-company housing is done by word of mouth (a person has stayed there before and returns, or sends the info along to their friends, etc.) The CM on the tours *might* share the information but I imagine they'd have to worry about being liable (what if the place ends up being shady and it was "recommended" by the company manager...) Plus, they've already got plenty of work to do arranging regular Company Housing - they don't want to field all the non-company housing options too.
A lot of people seek housing on Airbnb, VRBO, etc. (include in your posting that you are a theatre person as well). You could post the information at the theatres in the cities (won't help for this time, but they'll note the info for the next time they are thru or can pass the info on to friends who will be thru soon.) Social media/Facebook - NYC, Chicago & LA have Gypsy housing pages. Post on forums like this...