Later that day Garmin released an update, and one of the fixes was that very issue.
So today I gave it a second try, and it's still broken! My watch cannot end the session. I'm going to have to reset everything again and lose what little data I'd managed to build up! Arggghhhhhhhhhhh

Any ideas on what else I can do to avoid a reset? Last time somebody said they fixed it by starting a second LiveTrack session, but that isn't working either.