Hi, I'm Molly's owner - ie: Medicating Molly thread.
You have a lot of good advice here, already. I'm going to give some that may be a bit... off the beaten regular path, but it's based on nothing but my own experience with a pretty issue-y dog.
But first let me say no, I don't believe this situation is hopeless. The fact that the dog has made contact and not broken skin is, like mentioned, good bite inhibition and that's a good sign. It means the dog wants things to stop, but doesn't actually want to hurt anyone. Again: This is GOOD.
I FULLY agree that seeing a behaviorist is a good idea.
Here's where I'm going to go off the standard advice.
Get out of classes. Don't worry about going in public or other locations, at all. Seriously, give this dog a solid month, maybe two, letting him decompress. This applies with or without meds. Work on training, yeah, but super easy or super necessary things. Train to bond and build trust and to learn to work with you, not to fix behavior (for now). Reward eye contact. Work on sit and nose touches to your palm. Maybe train a really ridiculous trick like 'say hi'. LOOK INTO SHAPING - if you can train him without touching or physically manipulating him, you will have extra trust. You're going to need that.
If you get and start meds, this is 'loading time'. If you don't, it will still help him come off edge. He really needs to see you as a source of security and trust and to have a line of communication with you before you can ask him to do things he finds stressful or hard, either way.
Second, impulse control. Look up 'it's your choice' and teach that and play with it. Those can be your silly tricks and low pressure training at lower levels and will give you a foundation. Third: Reward calm at home.
But mostly, give him 4-8 weeks of just BEING in your home, with no pressure, where you work hard on bonding with him and earning trust and building a desire to do things with you.
Then start obedience training as you are. At home. Fluid, simple, things like sit, down, loose leash walking (or use a no pull harness). Once you'v got that, yeah, start with public. With distance. With zero interaction with the public. Get him a vest or just tell people to ignore him no matter what and don't allow petting, feeding treats, or anything else. Make people furniture, not important to him right now.
But I think the most important thing you can do for this dog right now is let him decompress for a while, bond with him, encourage him to bond with you, and learn each other. This is going to be a months long process, almost no matter what. A few weeks to let him chill some more and figure out how to interact with you better than he's got now (and I'd had my dog from 8 weeks to 18 months and she needed this) isn't going to make any huge difference in the timeline but probably well in his mental/emotional state.
Which I guess is the last thing: You're not training like you think of it with another dog. The goal isn't to perform a behavior on a cue. The goal with this isn't 'DON"T BEHAVE THAT WAY" because the behavior can stop and still have an unstable, stressed, dog. Your goal here is to be able to say, somehow, to the dog 'This is okay, and I've got your back, you can relax' and have the dog understand and to trust you enough believe that.
I know that sounds very twee, and I'm sorry for that, but it's still what the bottom line amounts to. Dog's got an emotional issue, not a behavioral one. Changing the behavior is almost impossible if you can't get to the emotional state, and even if you do the emotional state's still an issue.
...if you have specific questions I'll be happy to answer. I'm sorry if this is incoherent. I'm feverish and sick and rambling in circles.