Thanks again for the input and ideas. No slow drain problems - sinks or shower. Blockage idea must be explored, it seems. No clean out nearby. I do have a small drain auger I could try passing into shower drain.
Our shower stall is in a corner of the room, made of individual boards/panels of what I have always called "cultured marble" (fiberglass?). When we first bought the house (14+ years ago), there was a problem with water collecting under the shower floor, probably from a failing caulk seal around the perimeter of the floor. The floor panel was set onto what looked to be mortar mix or just sand. Man - did that water stink! I hired some guys to fix it and they did a great job - pouring resin in under the floor panel. It's solid now and caulk is still secure. I'm pretty certain the smell is not from standing water under the shower floor panel.
After sopping the standing water in the drain, the smell disappeared. Then I ran the sink, the shower drain level rose a few inches, and smell returned - almost like the sink draining was pushing stuff into the shower trap (if it is one). So I cleaned the sink trap (smelly but not clogged), then flushed clean water for a minute or so. Saw slight turbulence in standing water in the shower drain, but no smell. And this morning, there was no smell from the shower drain, which is not the usual case.
Could the problem have been as simple as needing to clean out the sink trap?