According to Joe Oldham (look him up if you aren't familiar) he considers a 1973 Camaro Z28 with the L-82 (350) engine, as a muscle car. Also the 1976 455 HO Pontiac Trans Am one as well.
He kinda knows what he talking about...........spent his life around muscle cars.
If the mount isn't the problem, then you might want to take a look at the transmission vacuum modulator to see if the rubber hose is cracked, loose or something. that could cause hard shifts too. Or the modulator or more could be shot from too many burnouts.
Yeah like 72ChevelleOhio asked - what are 305 race headers anyway?