Have you tried
Pawsitivity Service Dogs? They say they serve both veterans and civilians in their section on PTSD.
Owner-training is an option in the US, though I'd recommend finding a trainer who is experienced with training service dogs (
here is an example - don't know the trainer, just that they explicitly talk about training service dogs on their site). I know some will help evaluate service dog prospects as well, whether you're adopting from a shelter or looking at a litter. This is frequently more expensive, and you'll be doing a lot of the foundational training (with the trainer's guidance), so it's very different from going through a charity. But it also allows you flexibility in deciding what tasks you need trained and how your train them, and it means avoiding the wait list many charitable organizations have. Definitely not an option for everyone, but it is absolutely legal to do in the US, and your dog will be just as much a service dog in the eyes of the law as one from a charity or program.