John Jones, a fellow Cessna Pilots Ass'n member, has put me on the right
track, I believe. The autopilot receives its altitude information via Gray
code from the Garmin transponder. If a particular line is grounded, it
would hold the autopilot at 13,000 ft.

Tomorrow I'll take this information to the avionics shop and see what they
say.

That wasn't it. The incorrect altitude Gray code is definitely coming from
the Garmin side.