The problem "was" the dog park! That's why your not going to find a lot of pro dog park folks around here.
You have pretty much outlined the perfect way to create a dog reactive dog! Your job is to protect your dog from bad experiences,not only did you not do that but you put him in circumstances where he could get punked!
Then when he tried to protect what was his...he gets corrected! He's reactive to others dogs now because he feels he needs to protect himself because you haven't!
So uh no it's not bad genes.
Now you have to rebuild a relationship of trust with this dog, dump your trainer and find some one qualified.
I don't know if this dog will ever be able to be a "dog park dog" but he can be retained to be civil around other dogs.
Basically treat, ignore and move on. Avoid other dogs, on a walk no more dog parks! Your goal now is to reestablish a relationship of trust with your dog.
Treat and ignore is now your goal. When your dog sees another dog give him a treat so he focuses on you. Don't get close enough to other dogs for him to strike! Your goal is not making friends.
He gets a treat for ignoring other dogs and if he locks on them turn around or cross the street break focus, Your goal now is for him to ignore other dogs and focus on you! That's the essence of what you want to do.
You actually did pretty good with the dog park ,all you got out it is a badly socialized dog, you could have done worse...
Leerburg | Dog Parks: Why They Are A Bad Idea