Did you try aggressively leaning while having full carb heat? Possibly
your engine was flooding out from an iced carb venturi. You mentioned
going to full rich, but if it is an icing situation, it may instead
require further leaning with carb heat on and full throttle to get
enough heat in the exhaust system to melt the intake ice. It won't
necessarily melt out right away either, and I assume you had carb heat
on for enough time to clear out any ice It might take say 15 seconds
minimum. When the ice melts, the engine will go rough again until you
set things richer.

Another remote possibility is a valve sticking open. Usually that
happens on startup, and I have never experienced it. That engine has
some history of having sticking problems. You were not that far from
the last major and I assume the oil was reasonably clean so that might
rule that possibility out. Q - was it one cylinder missing (i. e. a
stuck valve) or was it a general engine malaise (mixture problems)?

Mixture and ice problems are why I really like having an EGT to cross
check the combustion and the energy extraction process.

Actually a 4 cyl engine running on three cylinders for whatever reason
will only generate about 50% power and will feel very rough. However,
it can still extend your glide a long long way.

Congrats on making it down OK. The first engine failure is the worst.
Next time won't seem so bad.........!