I'd be prepared to call for the AMA not to have a monopoly on their certification and licensing. As it is, we bypass them anyway by importing a bunch of doctors who went to med schools in the Caribbean. Why not run more U.S. med schools instead? At the very least, increase the number of med-school slots in line with population growth; there are now fewer med-school slots per capita than there were in 1980, because the AMA refused to allow any new med schools to open between 1982 and 2001, and has put strict limits on enrollments at existing schools. Throughout the 80s and 90s they justified this with dire predictions of a "glut" of doctors, which of course turned out to be incorrect.
Sounds fair, but that concerns the amount of people licensed, not the requirement to be licensed in the first place.
If you create an AMA2 while maintaining present licensing standards, you're simply moving the ultimate responsibility for guarding the standards from AMA and AMA2 to an entity above them.