I'm thinking that it sounds like the engine is running out of fuel. Perhaps you should check out the whole fuel delivery system, starting with the filter.

EDIT
With carby ice, what happens is that the air passages in the caeb freeze up & becoome blocked. This results in a rich mixture & lots of black smoke, so this is something to look for.
Backfiring through the carb is a sign of a lean mixture, while backfiring through the exhaust coule be a result of an excessively rich mix.

All efficiently operating carby's will feel cold around the base, but frozen ones will frequently have some frost or ice around the throttle area. The better the state of tune, the more efficient the engine, & the lighter the throttle setting at cruise, the more chance there is for ice, but usually only in cold & humid condidions, ........ usually.