I couldn't agree more! (everyone has to "go" every now & then; )
But to apply my expertise to the OP's question.............first of all, just about any time I'm "out & about", it's a 95% chance I'll be in good old Terre Haute, In. I'm very "selective" as to where I "drop my pants" (for any reason ), and any time I have this need while in TH, I will almost always go to one of two places; #1 is a Union Hospital; I'm totally familiar with ALL public facilities at UH, and I can always count of world-class cleanliness at UH; also, the other folks you're apt to encounter in a public rest room at UH is generally way above average.
Also........because I'm also very "into" photography, I happen to have something that's called a "Clik Elite Body Link" which is essentially a small pack designed to carry a full size D-SLR with a 70-200 mm zoom lens, and has a harness that allows it to be worn either as a back-pack or a chest-pack; I generally keep it in my car, (empty), and anytime I'm going to need to have my pants down, my G-34 (and anything that may fall out of my pockets, like car keys, wallet, loose quarters, etc go in the pack and stay on my chest while I'm "busy".
No laying valuables down on the floor, toilet tank, or any place else for me; I left my wallet on a sink counter in a service station once when I was getting out of my dress blues and into my levis and MC boots one time while I was in the Navy in 1952; I discovered I was missing my wallet 20 minutes later, took 10 minutes to return, and my wallet was still where I left it after half an hour! You don't get that lucky more than twice in a lifetime.
In certain circumstances I carry my G-34 in the chest pack; if the need arises, I can have it on-target quicker from there than I can from my IWB holster and no shirt to mess with.