I would be interested in how you get the horse to never need to stop and look.
Specifically. My experience with Mac has been that if I force him forward, when he has not yet processed what the scary thing it, then he has "blown" , and he goes from being tense to 180 degrees the other direction so fast it's amazing. Since I started allowing him to stop and look or listen, he has not spun on me. I do not allow him to stop and look at everything, tho.
I am not the rider you are, I don't have a lifetime of experience. I didn't grow up on horseback. But if you explain the method you use for these police horse, well, I might learn something.