Sorry to hear of your son's shoulder injury. Good news is he's not a PO, has a solid academic resume, size and respectable speed. Unfortunately my son has some experience with the labrum surgery timeline. Coincidentally he also did a PG year, unrelated to the labrum injury though. But I'm sure you're aware that recovery from labrum surgery takes 12-18 months, give or take based on degree of tear, whether PO or DH, etc.
So let's say your son has labrum surgery January 1, 2020. In theory, he should be able to throw on a limited basis by June 1. Again, that's limited throwing, under supervision, and restrictions. If he did a PG year, (extra year of HS) he could possibly be DH'ing for fall ball to get some looks. By March 2021 he could be playing LF or RF and throwing at game speed. But the spring season for a PG year in baseball won't do much to draw attention as the recruiting window will have ended by then. He will need the fall ball season for showcases and camps to get looks. Definitely stay in touch with current coaches who've shown interest already, they'll be best bet as they'll be willing to credit him the level of play they witnessed with their own eyes pre-surgery. Unless he's able to rake with the bat in fall ball 2020, he may not draw any new interest due to the surgery.
Being game ready in September, only 8-months post surgery, may not be doable. My experience is with POs and if he were a PO there no way. But DH'ing I'd say good chance, but being able to truly throw at 100% won't be till after 12-months, depending on the level of surgery (# of anchors inserted for example). Mine is now approaching 14-months post labrum surgery and I'd say he's at about 80% throwing capacity (velo and endurance). Still needs to be careful and limited in what he does. Definitely still in cautious mode.
The application timeline for PG years is approaching. Most deadlines are in January I believe with notifications going out in March.
Hope this helps. Best of luck to your son.