Beaufort is covered by the USCG. New River doesn't need dedicated SAR--it's a helo base. Cherry Point still needs it. As far as range sweeps, it's a good collateral job for those guys, but not enough to justify maintaining a dedicated platform--and if that dedicated platform was a V-22, not enough to justify multiple $50 mil + aircraft.
My personal opinion is that the mission will go away after the last fleet CH-46Es are gone. It'll be too much effort to maintain dedicated parts and logistics support for a small number of aircraft, not to mention that the number of Marines qualified to crew and maintain 46s will progressively shrink.
You'll see some sort of combination of LOAs between the USMC, USCG, NC State assets, and private LifeFlight or SAR to cover the duty. As the USMC shrinks down again, they'll want to put active duty Marines in line units v. supporting establishment.