I’m in no way trained in issues around psychology, and scream like a woman if there’s a spider in the room bigger than ten pence piece. But i think exposure. Not in public to begin with, I’d volunteer myself and my very friendly,(but trained so under control) goldie if you were near by. Very short periods of time to begin with. Maybe 30 seconds in the same room. or watch someone playing with a dog from a distance. He probably needs to learn in a subconscious way that a dog can cavort about and jump and run, and he can be fine. Not sure if he should know its going to happen or not, someone else may be able to advise tbw.
It sounds like you may be on the money with the great dane if it is dogs moving that upset him, sudden unpredictable movements may trigger a small adrenalin release .
The other thing would be not to exhibit yourself any behaviour that reinforces his phobia, picking him up the moment their’s a dog will seem like you think there a reason he needs to be protected. Fine if he asks but make him initiate it. Let him see you talking to and playing with dogs. No quick fix, but with your help I’m sure he can grow out of it.
Probably all stuff you’ve thought of but its how my mum stopped me picking up her phobia for thunder , and why i now run outside in a storm and stare at the sky when lightening begins, so get it right and maybe he’ll be a vet ;) (i did get my spider phobia from my sister, i remember being fine with spiders)