did you leakdown test after assembling this new setup? based of symptoms, maybe clutch side crank seal is pulling in trans oil (i know you said you looked at it) which could explain the wet plug and dripping oil. Ive never experienced this so not sure if this would explain the piston being clean but worth a check.
If leakdown test passes and since it happened after sitting for a few weeks, clean out all circuits in both carbs, ensure jets are cleaned out and they match, and verify still synced then retest.