Hi Dee,
Welcome to the community!
See my answers below, and let me know if you have more questions.
Since their behavior escalates to the point of the situation getting out of control, you should work on overall off-leash control away from the park using other distractions first. If you use dogs that your dogs are more comfortable with in a smaller area, you can start more slowly and identify trouble spots that elicit an inappropriate response in your dogs or loss of control such as when dogs move more quickly, play with each other other bark.
Make sure also that their overall reactivity is lowered throughout the day, and they are not building barrier frustration when at your home. This can cause more reactivity at the dog park.
My favorite counter strategy to reactive off-leash dogs is to teach them a rock solid Stop cue. If you don't know how to teach this, you can learn from my Stop video which shows how to teach off leash control. You can see a sample here. Emergency STOP! Sample
Here are some other posts that might be helpful.
Dog Park Body Language
Dog-Dog Aggression at the Dog Park Forum Question
Dog Park Training Tips (Episode From My Radio Show)
Good luck, and keep the community posted on the progress.