If you want to do something of lasting value to vets with CRPTSD, you are going to have to make a commitment beyond doing "something nice". The personal rewards can be enormous, but the personal investment has to be deep. This can be a difficult population to reach; cautious, untrusting, tough and fragile, proud but needy, wanting but often unable to make a commitment. I find that what I believe is the core of of my Aikido enables me to remain centered and open, with no expectations, no anticipation beyond my own commitment.
The only thing I would add to this is that the benefits you do are not always obvious. You might want to share that with the recreation director, who seems to feel (not unreasonably) that if no one participates, they're not getting any benefit. Sure, they're not getting all the benefit they might...but someone in this state does receive a benefit from your act of reaching out and offering. It's part of the healing process, I think, and essential to learning to trust the world again: to know, to have it repeated no matter what your response, that people are offering, that they want you -- YOU, just as you are, all knotted-up and hurt. And it's especially important to have those offers come from those who have some distance. When people are traumatized, they (and we) tend to think that most of the help will come from those closest to them. Well, maybe it does, in many cases...but just because someone is close, doesn't mean they are best equipped to help, particularly when the person they're trying to help may sometimes refuse it -- that puts strain on the relationship, in both directions. Sometimes someone isn't yet ready to accept the help that is offered; refusing/rejecting a loved one carries a lot of baggage with it, that may make it a lot harder to go back to that same source later and say, "Is the offer still open?" You're doing more than you know, Tom, just by offering with a calm spirit and open heart. No matter how many people come onto the mat, you're doing a lot.