Yes would strip it of all the paint, do the needed repairs then repaint it as originally done.
Since the black paint itself is textured that should provide you with a nice original looking finish when done. Of course do a spray out of the paint first on something else as a test so you can get the pressure and other details worked out before you spray the spoiler. As with many of these finishes we try and reproduce its product and technique that gets the job done.
Final "look" should be a low shine like modern "egg shell" in most cases
As for specific product, laws and availability change all the time as to what is available and legal in different parts of the US and other countries. Did do a search on this site and found the original product or repair paint to be
And found this longer threads (out of maybe a half dozen) that listed a number of products people had used at the time of the posting. Just used the words "70 textured black paint"
https://www.concoursmustang.com/forum/index.php?topic=22817.msg142963#msg142963
