2 y/o Lab/Retriever/Shepherd cross is reactive to other dogs, resorts to aggression

I am at a loss of what to do at the moment. My dog is a rescue that I bought from the SPCA 4 months ago. His background is mostly unknown but from the behaviours he's displayed he is very reactive to animals and humans with dark skin. I believe that he was a reserve dog and was raised by an abusive aboriginal family around other dogs that would attack him.

My issue is that when he becomes reactive I have no way to leverage anything over him for him to listen to me.

He has very bad allergies and it's almost definitely to food. I've just started him on an an-allergenic diet as he has been having reactions to every food I've given him thus far.

He's not very food motivated because most treats give him allergic reactions. After about 5-6 treats he will start to refuse them.

I've been training him mostly with affection training, but it's definitely not as effective as food is... when he likes the food. But I can't give him anything now because I have to rule out allergies.

When he's meeting dogs he gets extremely reactive. Most of the time it's playful, but the instant he sees any fear or aggression out of the other dog he attacks. I usually can stop him quickly, but it's getting out of hand.

At one point I became abusive and would smack his nose whenever he attacked other dogs because I had nothing else I knew I could do to punish that behaviour, but obviously it's just made him more aggressive to dogs.

I'm no longer hitting him, I've stopped using the choke chain he came with, and he still becomes aggressive and refuses to listen to me whenever another dog is within 10ft of him.

I don't know what to do anymore to fix this behavior. He used to have dog friends but I just moved and now I don't even have friends, let alone friends with dogs who would put up with him.

Help :(