I will only allow people to approach him after making sure that I'm in an environment where he can be distracted, due to a very low risk of me needing him. I don't know what your experiences are with service dogs, but for the most part, the ones I've known tend to revert to "pet mode" either when their owner gives them permission or when their vest is taken off. They're dogs, not machines, and socialization and affection are still important for them even though they have a job to do.
As I said, I prefer not to impose on people and businesses whenever possible and avoid bringing him places that wouldn't welcome any other dog unless I have no choice because, although I am afforded the same legal rights as someone with, for example, a diabetes dog, I'm aware that it's not as urgent and life threatening of a need. We sit outside at almost all restaurants, and if I must go someplace where I feel he wouldn't be welcome I prepare myself ahead of time or make sure I'm with people who know my condition and can help if a situation arises. Luckily I live in a very dog friendly city where he is welcome almost everywhere.
I haven't decided how I'm going to handle GSMNP -- I will probably decide to kennel him or bring him through with me after seeing how I fare up until that point, but my hunch is that I'll be ok since the trail is far from having any resemblance to the source of my trauma.