IIRC a small number of Unlimited Mustang racers had ex-Shack Griffons in the 70s/80s, but certainly no factory machines.
As far as Korea goes, there are no records of F-51s shooting down jets. Mustangs scored several kills early on against Yak-3/9s and Il-10s - maybe a Po-2 or two, but the only piston-engined fighters to score against MiGs were the Sea Fury (one definite, a second maybe, as mentioned above) and the Corsair, which got one.