So, does everyone agree that induction icing, more specifically, air filter
icing was the likely culprit?  If so, why doesn't this happen more often,
since air filters are universal, and some, like Cessna, are right in front in
the open?  Could it be an installation problem in my case?

Ed,

 

Nice job of getting back on the ground so that you could relate this event to us.

 

Working backwards, carbureted Cessnas have carb heat air available and injected ones have an alternate air door (automatic, spring loaded).

 

Sure seems like induction air blockage, where the throttle position (WOT?) does not match the little amount of air available and the 4 venturi tubes in the throttle body are not seeing much air go by so the fuel flow is reduced.  The hiccups may have been from water passing thru the system.  Reducing the throttle was a better match to the air leaking into the system.  Remember that at idle, the throttle plate is almost completely closed.

 

Airflow into the engine cooling plenum is different during climb and maybe that allowed rain to collect or soak the filter that then became frozen?  It would seem that you usually fly thru rain on ram air.

 

I think you must consider the ram air as the "alternate" air source during any engine difficulty. You are the spring!