Tim Carolan, a bike fitter in Tucson, leads a "shop ride" out of Cyclefit Solutions every week, I haven't gone on it yet but my friend who has insists it is
very chill...definitely the antithesis of the Shootout! I think you can find more info here:
https://www.facebook.com/timcarolan [edit: disregard, see my post #7, below]
Speaking of which, Sabino Cycles leads a weekly early ride from the shopping center on the north-west corner of Catalina Hwy & Tanque Verde Rd up Mt Lemmon just to the Molino Canyon Vista & back. 20 miles round trip, "conversational pace" (whatever that means when you're climbing a 6% grade for 5 miles). Can't remember if that's on Fridays or Saturdays.