Gary,
I'm not sure if you are referring to processing that print as a regular salted POP or trying to develop it, but, with the regular POP process you need to tone the print with a gold or platinum/palladium toner formula before the fixing step. Otherwise the print will bleach considerably in the fixer as you describe. Also, the fixer for POP processes is generally much weaker than conventional silver gelatin process fixers. Rapid fixers are out as is toning with Kodak Rapid Selenium Toner which is compounded with high percentage of ammonium thiosulfate aka rapid fix. Weak solutions of sodium thiosulfate aka "hypo" are generally used for the silver alternative processes. Hypo solution strengths are generally around the 2% mark although sometimes the strength is higher (I've seen it up to 15%) and sodium carbonate is added to the plain hypo fixing bath to make it alkaline in order to reduce the bleaching problem.
Don't know about the after process fogging. Was the clearing agent Kodak Hypo Clearing Agent (primarily sodium sulfite) or something else?
IIRC, another thing to try is adding some table salt to the initial rinse. This apparently helps remove the excess unexposed silver. Before trying this or the alkaline fixer though I would try to find a reference either on the web or in a standard alternative process text to determine the strength and duration needed.
You might also try a different paper for salt printing and other processes. I've found Arches Aquarelle to be inconsistent and prone to uneveness with alternative photographic processes. Give Cranes' Cover, Kid Finish, or one of the better Bristol papers a shot with salted paper.
Joe