There's Tuesday Night Steel every Tuesday at Rio Salado (http://www.rsscaz.com/divisions/tns/) and Steel Challenge 3rd Sunday at Ben Avery (http://cactusmatch.com/index.php/match-desc), the Cactus Thursday night matches have a mix of paper and steel.Not sure how you're distinguishing between competition and "competitive fun", but if you're just looking for a good time they're all good matches and not high pressure competition or anything.
I have ar500 steel and paper targets/stands as well as a shot timer if you want to setup a friendly competition course in florence some time. Always looking for like minded people to train with. Im ordering a few rubber dummies pretty soon too.
Well I've seen the entry lists and times at Rio Salado, to me that's a little intimidating. Especially going in by myself.