Jed,
Sorry for the slow reply. Yes, the jams might work for you. They're primarily trad. stuff, and tunes more than singing (though we singers are making some inroads!).
Also, Bookmans, a big used bookstore, has just started open mic nights on 1st, 2nd, and 3rd Tuesdays. This conflicts with the jam, but if you want to sing your own stuff rather than "play tunes" then that might work better. They're at 1930 E. Grant Rd. (at Campbell Ave.) Info from Dennis or Bruce at 325-5767. Play from 7 to 9:30 for 12 minutes each. Sign up from 6:45.
~ Becky in Tucson also, that TFTM e-mail address goes directly to me