Yikes, I would pass on your gym.  I agree, you might want to find another place to manly up.  At least find one with more than one throne. 
 
It shall never cease to  amaze me what sorts of projects men create in the confines of the public loo.  I've seen some things, but must admit, never any testacular spelunking onto the D ring like that.  I suppose that's why they provide those paper life-preserver thingies on the wall, though I'm pretty sure you'd need 7800 of them for THAT joyous mess. (Do they have a Scott's version of those seat-cover, bum-germ thingies?)
 
I once stood waiting outside the sitter in pain at a highway "rest area", while some chap reeled off about 25 km of paperwork in the little horse stall.  Spun that thing for minutes on end, time after time. I wondered, "what on EARTH are you going to DO with all that paper, and what is up in there"?  Then realized I didn't really WANT to know.   Good lord, we are amazing creatures indeed. 

Good luck in your search. Maybe you could ask at the front desk as you make your rounds to switch sites, about these sorts of activities from the outset. Then again...