Whoopi! My Cooper is back, and it is running great once again. Two main problems were found; one valve was much too tight (why? Let's hope there won't be a sequel to this episode) and there was no damper oil in the carb.
Come to think of it, they let it drain at MiniSport when the car was
there for a rolling road tune, but we never saw them fill it back up
(in al honesty, rolling road tuning wasn't this guy's regular job;
something went wrong with the appointment, so they had to find a
replacement).
Anyway, it turns out it was actually running quite well, considering
the circumstances... It's back to normal now, though. There'a Vernier
timing gear ordered, which will allow the valve timing to be set spot
on. Maybe also some upgrades to the ignition system, and then we should
be off to SpeedCentre Geldermalsen for another tune-up.