Tiling began yesterday. Now the bathroom proper and the shower stall (not pictured, but it has 2"x2" gray tile on its floor) both have a floor. I couldn't walk on it last night, so pictures are limited. These tiles are a medium gray and have a slightly rough surface texture, so they won't be slick or slippery.
We've also got a new, small window (that opens!) and the beginnings of proper, non-makeshift venting for our clothes dryer and future exhaust fan.
Tiling is continuing today. Rumor has it that that bathroom will be complete by the end of the week. Time will tell!