OK, got some new results. See data logs FLY081.DAT and FLY082.DAT at the link below.
P4A data files - Google Drive
FLY081 was a short 3:34 min flight after calibrating IMUs only. I terminated the flight after receiving "compass error", and "weak GPS signal" messages at 1:33 min. I also got a couple of "Current RTH route will pass a No-Fly zone. Pay attention to the aircraft's position to avoid RTH failure". I never initiated RTH and there was no other indication that the AC self-initiated it. Just alot of confusing disconnected pieces of info.
Then calibrated the compass out in the middle of the soccer field. After calibration, the compass interference values were as shown in the pic below. Sorry I didn't think to take a picture before calibrating, but I recall the bars were green but somewhat larger than shown here. The point is, relying on the app to judge compass health ain't no good.
While preparing to take off, I got this warning on the Aircraft Status screen. I figured, oh oh, now I'm getting the error before takeoff, and contemplated not even conducting another test, but then realized this might be a hangover message from the previous flight. So...cautiously, I took off.
FLY082 went uneventfully, staying in GPS mode all the time for a 12:48m flight, with none of the aforementioned errors. Continued with VLOS and low level (up to 100 ft) with no issues. Contemplated doing a POI circle as a test (it makes better circles than I do) but didn't want to push my luck until having had a chance to confirm the data is clean.
I'm now a believer in calibrating and not trusting to the app for guidance. I'm very grateful for all the advice and analysis the dedicated individuals on this thread have provided. Before I celebrate, I'll wait until the experts have weighed in and confirm that FLY082 is "normal".