The USAAF always used the "P" for "Pursuit" designation. After the USAF became a separate service in 1947, they revamped the designation system, and changed it to "F" for "Fighter." The USAAF had designated recon aircraft "F" for "Foto"..Under the new USAF system, this was changed to "R" for "Reconnaissance." The USAAF had used "R" for "Restricted," usually applied to combat types used in various utility/training roles. That designation was dropped entirely by the USAF. Hopefully that didn't leave you "C" for "Confused!"
I don't think the change had anything directly to do with SAC, which was one of several different commands set up by the new USAF.
SN