Is this carbon buildup? And how can I fix this?

Post 1, third sentence. It pops when he steps down on it.
To me that means a back fire thru the carb. That will build carbon deposits from the cylinder to the air cleaner faster than you can imagine.
Yes but that's not one in was referring to. Again. only 2 out of the list are even relevant.

Timing, it's more than likely high initial on manifold vacuum as mattax pointed out.
Lean pops can occur with too little pump shot or really high initial lighting it up through the intake manifold.
Too much pump shot can make boggy sooty mess as well...and that can catch and back fire too on the extreme end.
My advice it to start from scratch on the tune, get the ported vac hooked up, timing/curve right and then tune the transition...if it's bad still, plugs look good and not FOULED then look for mechanical failure of some kind.
He was just throwing everything you could at it for reasons to be
Happy hunting.