"if the plumbing is behind layers of 1/2" cement backer board, paint on waterproofing (black waterproofing paint completely covers 1/2" backer board), the pan liner, and tile, how would water get to the inside of the shower pan and wick through the grout?" When I posted I didn't know how your shower was constructed. But if you have a topical waterproofing on your cement board and a pan liner on the floor, the pan liner membrane goes down and gets lapped up the walls 8" to 10" and gets stapled to the studs. The cement board on the walls goes over the pan liner. If there was a leak behind the wall, it could spray on the back of the cement board. It could run down the cement board and go between the cement board and the pan liner, wetting the mud in the floor. I'm not saying that is what's happening. But it's an option. I've seen it before. And you are correct, a water leak behind the wall could show itself in a ceiling below. With the "new news" that the grout is cracked, yes, water could be getting into that crack, thus the slow drying at that joint. In lightweight shower construction, changes in plane (wall-to-wall and wall-to-floor) should be caulked instead of grouted. The surfaces can move independently of one another. Caulk will flex with the movement, grout can crack. Also, if he used a "pan liner", it should have been set on sloped deck mud. Not flat on the subfloor, with sloped mud on top of the flat liner. The flat liner can cause moisture that gets under the tile (through your cracked grout for example) to pond. It can show as damp grout lines that are slow to dry. If the liner was sloped as required by code (which yours may be), the moisture will hit the sloped liner and flow towards the drain. If he used a topical membrane on the walls and on the floor instead of a pan liner on the floor, then all of the above is pretty much non-applicable. With a topical membrane on all shower surfaces, it's probably just latent water running down the shower head wall, or the crack in the grout storing water and being slow to dry.

@derauf Permanent Press is the cycle that doesn't run Eco Active recirculation. Did you remove and examine the diverter for a broken linkage, or a foreign object jamming it from physically shifting modes? Assuming your pump runs and the diverter is not broken or jammed, a cause of continuous recirculation (failure to drain) is a bad motor controller board that continuously powers the diverter, per the previous replies to Greg Neault in this thread. Using Permanent Press won't circumvent that problem because the board is bad and powers the diverter at all times regardless of the selected cycle. A possible work-around is via disconnecting the diverter wires. Permanent Press is the only cycle that would work that way. The motor board would run the pump during recirculation periods on the other cycles which would drain the water even if the diverter is disconnected.

I'm pretty positive not. There are only 11 units; only 9 resident families (one's a duplex; one's empty). There's no room in the units to be installing devices; it's pretty tight. My big question isn't really "what's causing this?" bcs I'm pretty sure the plumber will figure it out. (I think it's a check-valve that has gone bad; we had the same problem 10 years ago when the plumber put in new water heaters & put the valve in backwards. He fixed that--but this problem is SO much like it, that's my theory--a failing check valve) But I'm just wondering--does it really matter whether you turn the shower diverter down AFTER you turn off the faucet at the handles, or BEFORE? I always thought it didn't matter, and I'd like to confirm it.

The problem could be at the shower hose connection. Remove the hose and escutcheon to look for evidence of a leak. It could also be a problem with caulking of the tub surround if the hand shower sprays where there's a gap. If you still don't find a leak, you're probably going to need to find a way to look behind the wall at the pipe leading from the diverter valve to the shower hose connection.