You will have problems. First, breed restrictions exist for a reason. Many insurance policies will not cover losses caused by restricted breeds. Second, many people are afraid of those same restricted breeds and the presence of those dogs in a park makes other guests uncomfortable.
As for multiple dogs, there has to be some limit. Two generally is the norm. Each additional dog creates more noise, waste and multiple dogs are harder for an individual to control by definition. You will find you will get more exceptions for the multiple dogs than you will for the restricted breeds.
One more note, when you say you have "terrier mix", most park owners will assume you have a pit bull. That term has become a code to try and avoid breed restrictions. If your dog was a rat terrier or Jack Russell terrier mix, you would say that. We would never make an exception to our breed restrictions for someone traveling with both a Rottweiler and a pit bull. Just too much risk for us and too much drama for other guests.