Sorry for the delay, everyone, but this morning's ride was the first one in the past week that was long enough for a rest (read: breakfast) stop. Turning off "auto power down" and turning on "auto pause" seemed to do the trick. No spurious elevation readings at the stop. I left the Garmin on the bike, parked in the sun as usual, and all the report showed was the expected bump in temperature.
Here's the correction-enabled Garmin elevations graph:
And here's the same from Strava: