How exactly does one determine during flight that his rough-running engine
is
caused by a dropped exhaust valve as opposed to something more serious
that
would not last very long if left at full power?

No hard/fast rules. The general rule of thumb would be to check for
confirming signs of imminent failure (oil pressure, cyl head temp, etc.) and
if you have confirmation that the engine is about to suffer a general
failure, then you probably want to consider a forced landing. But
otherwise, and assuming the vibration isn't so bad as to threaten engine
mounts and the like, continue to push the engine for what you need to get to
the nearest airport while maintaining altitude.

In this case, a GEM would have been a nice thing to have. It would have
shown that one cylinder had failed and the others were still making power.
It would have confirmed the the rough engine was basically because one
cylinder was off-line. With this confirmation, you'd be confident to push
the remaining three cylinders as hard as necessary to get to an airport.
I'd bet that this engine probably would have run for several hours with
enough power to maintain altitude. I'm not aware of a dropped exhaust valve
failure that has caused complete and immediate engine failure. These
engines are old technology, but they're incredibly tough with great reserves
of basic strength. Almost all cases of complete engine failure are fuel and
eletrical, not mechanical.

But we're all second-guessing. Allen did great. My only comment was a
general one: Be aware that many accidents are when pilots become so
pre-occupied with a minor emergency (which I'd rate this as) that they turn
it into a major one. Allen was so pre-occupied with conserving energy to
make the field that he almost had an accident due to an excess of energy.
This is just something we all need to watch for.

- Mark