If it were mine....
I'd tear it completely down for cleaning and new grease. While apart, I'get out my 0000 steel wool and barkeepers friend and do a complete rubdown (not over decals) of all the metal chrome pieces (not plastic parts). I make a paste, apply the paste by hand, then carefully rub out any rust followed by a hose bath and a quick dry. Pits will remain, but the good chrome will shine like new. Follow with wax for protection and it will really look nice. Cost is about $5 and some sweat equity but the results are amazing.