I suspect that it will be difficult to repair the panels. you could improve the appearance greatly by wrapping them in vinyl/leather and adding some padding to soften the lines. There are some fiberglass reproductions I believe, but I am unsure of their quality.
the UV light and time has made the plastic fall apart.
short of replacement with a trim panel in better shape there is not much you can do to make it look OEM.
the aftermarket reproduction quarter trim panels are complete garbage only good for a drag racer that needs to look like it has an interior.
1) replace it with a good original, very expensive, very rare.
2) you could smooth the panel, then either spray it the interior color you need, or buy textured winkle paint, spray it on let it wrinkle to kind of look like camera case finish then spray the correct interior color on top.
3) take the panels to a upholstery shop, they can make a camera case cover for the plastic panel like the older mustangs had, again expensive but will look much nicer.
Hey - honestly, I like my repop plastic interior trim pieces. After a coating of SEM metallic black interior paint, they look fine, and fit just fine after some adjustment (as with any repop item).
Keep in mind, I'm not a purist - restomod is more my style (I carpeted my package tray, after all ). Not having the ashtray on the passenger side, or even having a 100% perfect factory fit works just fine for me. My car will never seen MCA competition, and nobody's ever going to ride in the back, anyway.
Fifteen years ago when dashes and quarters were not available my dash pad had a couple wide cracks in it. I ground down the high spots and applied regular bondo over a eight by twelve area. Sanded that smooth with 180 grit paper. After that it needed something to look similar to the rest of the pad. I used Dupli-color truck bed coating, it provide a nice texture but the difference was noticeable, with 180 paper on a DA sander, I sanded off the tops of the drop like profile of the coating. I sprayed it with a Krylon color then clear coated it. It turned out great. I showed it a few years at MCA without being noticed until I got a NOS pad. I'm sure the coating will work on your quarters. It dries hard like plastic.
Just a suggestion. When I went to Dearborn to pick up a car a month or two back I found that interior parts up north are much better than from south or out west where the sun is so hot. I bought seats, and door panels that looked like new. they came out of rusted out cars that the salt ate up. So go looking up north on craigslist for interior panels and items that are hard to find in south or California were very reasonable there. I sold one set of the deluxe door panels on eBay for 4 times what I paid in Michigan and did nothing to them but wash. They were nearly perfect and were black, soft, no cracks, nothing missing and date code of 73 on the back. Got deluxe steering wheel with no cracks and everything there for much less than eBay. The consoles had not been painted and were almost perfect. Place your ads in the craigslist up north for what you need and let them call you. Even items like hoods and trunks are better than here in N.C. not as much rain and they were inside more than in south. They had zebart plugs in them where they had hot wax / oil sprayed inside so no rust.
I am going back to Michigan later this week or next and will load up again while there. Much better parts and better prices. Everyone raves about California or Arizona cars but it they were out in the sun much the interiors and anything plastic is toast. I have a 48,000 mile Calif. vert and the inner rear panels are like you describe crusty and flakey. I got one good one while in Michigan that was not crusty now to find another.