Sorry I didnt read fully the first post but I only have ideas no cure.
All my small motors have their own sequence in starting, to much choke
and thats it for a while, each one is different but my most expensive
Sthil is the best . You have to find what yours needs in relation to
choke. A weak yellow spark or bad plug, even new plugs come bad, bad
igniton module could be the cause. Champion has a new plug line that
says Easier starting. If plug is wet when trying a hot start while hot
check for spark with plug removed and its color and strength-length of
spark yellow is bad. I just had a plug wire not fire only when hot, but
fine cold. Ignition modules going bad usualy fail first when hot, even
a plug dropped can first fail only hot so check everything hot. Vapor
lock came to mind but you did say it plug is wet. Small motors, cheap
carbs and parts can be a pain. Be sure choke opens fully, throttle
closes fully and even lean the low speed mix. In the end it could just
be a crappy carburator.