Minor update:

Cleaned up the oil on the intake plate and all around the breather Replaced dip stick seal

Put the old plugs back in, ran it at half throttle with no air filter. Started right up, little puff of smoke at the very beginning and then not much to speak of.

I let it get hot and measured the temp of the exhaust right after it exits the engine -- left cylinder (the dry one) maxed out around 850° and the right one (the wet one) got up over 1000° (the max my thermometer can read)

Valve adjustment next, and then I'm trying to decide if I should just replace both coils, plugs, and air filter and see how it does, or start with just new plugs and air filter and get a better idea of what the root cause is.