"Running like it's missing"-misfiring at idle and under power?
"no power at any speed"- like a 50cc moped could outrun you, or just not achieving XX power?
Carbs appart 3 times trying to cure this, or in the past?
Yes, a rich mix can cause a cold burn, I assume by temperature you mean that exhaust pipe is colder?
Are there any vacuum hoses on #3 that aren't on the others? I'm thinking maybe the fuel valve and maybe it's leaking, or maybe a canister purge hose, or something else-I don't recall the vacuum hose set-up.
If not a hose issue-compression check, replace or at least swap the plugs around, test plug wires with an ohm meter.