What kind of paint, enamel or lacquer? Any paint stripper worth its' salt will eat the plastic too. There are many now that don't work for spit but leave the plastic alone. You can always try like Purple Power or Easy Off oven cleaner, what plastic modelers use to strip paint on plastic models without hurting the base plastic.

You cannot sand or glass blast plastic, the erosion friction melts it. Maybe VERY light glass bead might work but no guarantee there. Not the way to do it............ .....

Possibly. I know for sure you can't glass, BTDT, the results are 'less than satisfactory' we'll say. I know the modelers things work, I've done them on polystyrene before. The radio face will be close to that type plastic if factory Ford part.

Not aftermarket part is it? If like polypropylene (PP) you will never get paint to stick, it will not on oily base plastics. ALL plastics are oil based but some hold far more oil in the finished product than others, the oil effuses to delaminate all paint put on. Vinyl paint may work in that case, it flexes to help stick better.