I'm not an expert or even close when it comes to catching but I do know that although arm strength helps there isn't a one-to-one correlation between arm strength and pop time. My guess, given his build is that he may have a long throwing motion for a catcher and may need to shorten his motion and quicken his release. If the HS coach isn't already working with him on his technique, I'd suggest finding a catching instructor to work with him. That is what could yield relatively quick results.
Arm strength does of course help, but it takes an increase in velocity of about 20 mph to bring the pop time down by .3 seconds and there's little or no chance of doing that quickly. So focus on technique in the short term and arm strength over the long term.
As far as arm strength long toss is always good, and although there may be some risk involved, overload/underload training (weighted balls) might help. That's something you'll want to research and assess the risks before deciding to do it. If you do have him start up a long toss program, you'll have to be careful about having him maintain a catcher's arm action. Other than that, lower body weight work, core work and plyometrics can help.