I like the mass breeding route, save eggs until you have 60+ then hatch all at once, ready with your sword for slaughtering any non mutes. Best done by a grill to cook up the prime for jerky! Great xp too!
Its def not inbreeding like you can get it from inbreeding but you dont have a higher chance by inbreeding over not. Its rng bro up to the gods... i.e. our angler came out mutated first breed from two wild tames yet five rex generations in and no mutation