Job 1 radios (black knobs vs chrome Job 2) 6 disc & Shaker 500's, have a reputation of not working just as you described yours doing. There are places that offer these replacement pieces, but they aren't cheap and you still have the same radio, with the same problems possible again.
You might want to consider an aftermarket radio, or even upgrade to a factory navigation head. I went with a Ford Job 2 navigation head, installed a Boss 302 steering wheel (2013) and hooked up all the audio controls in the steering wheel. SYNC was added afterwards. It was a fun project.
Good luck with your new Mustang. Enjoy!!!!!
07 Mustang V6, GT 19'' wheels, Bullitt suspension & brakes, Dynomax dual exh w/GT takeoffs, Eleanor style grille, Shelby rear spoiler, CS/GT bumpers, SHR insert, side & rear window louvers, CS/GT scoops, SYNC/Navi, Roush hood scoop, Leather power seats, IUP w/GT MyColor, hood shocks, 8.8 trac-loc w/3:73 gears, logo'd trunk mat, trunk lid storage organizer. Gen 5 tail lights, '12 lighted vanities & outside mirrors, '13 Boss Strg Whl.w/audio controls, Ambient lighting, puddle lamps