Terk,
Sorry to hear about your son.
I hope all goes well in the decisions to be made.
At the outset, what you can receive from this site is, in effect, information that may help guide your decisions. IMO, the only advice you and your son should follow would be from the doctor, and a second opinion.
Coaches, friends, and others can't help.
With that said, I would tend to think the rehab and recovery time of 3-4 months is very optimistic.
For a labrum tear and surgical repair, you can start doing a combination of PT and strengthening at about 6 weeks. To regain a satisfactory range of motion and strength for baseball, you are likely looking at closer to 3-4 months, before your son can start throwing.
Throwing rehab can be variable but likely will have good days and set backs. You should likely plan on 8 weeks of throwing rehab. If your son gets lucky, great.
You should plan on 6 months for PT, rehab, strengthening, range of motion and throwing rehab. as opposed to 3-4.
Playing now, even as a DH, is a question of how much pain and instability he can endure combined with the risk of further injury/damage.
If you and your son want to maximize the opportunity his recovery will allow him to play as a junior in high school, you need to plan accordingly. Doctors, we have found, give things to hear that are mostly on the optimistic side.
Labral tears and repairs have much more variability in the timing and extent of recovery than TJ and other types of surgeries for baseball players.
One other item, when he has the surgery, make sure you know the surgeon and his experience with labral tears and baseball players. If you have any doubts, get a second opinion and have the surgery done by the doctor who has done these on baseball players, and has a track record of success.