Short answer is get ahold of either one of these outfits that really do a nice job:
D & M Restoration PH 864-254-9989 website: http://dandmrestoration.com/services/radio-repair/ Greenville, SC
Retro Radio Restoration PH 707-367-1428 website: https://retroradio.biz/ Elizabethtown, PA
Both can restore your radio like new or even upgrade the internals so that you have AM/FM and AUX capabilities to run music off your phone, but retain that stock look. I have done this on my last couple vehicles. My dash looks stock but I run my phone through the upgraded radio internals and listen to Spotify and even run my audio for my navigation through it. Pretty cool!
Reggie really nailed it. I would also suggest doing a "radio repair near me" search on Google as I have used two local repair facilities that do good work on factory stereos (even old stuff!) and you get the benefit of a quicker turnaround and the pleasure of supporting a local business. You might have the same good fortune as I do!