Should have added:
I think it also makes sense for me to have a break stick.
Jessie is actually quite used to having my hands in her mouth. When she was a puppy, she was a bit of a thief.

She'd grab things off coffee tables and such, and I, never knowing just what she had stolen, would grab her jaws, open them, and shake her head until her prize fell out of her mouth. (Yes, I am sure it looked as ridiculous as it sounds! ) Often it turned out to be earrings ( I had a bad habit of taking them off when I got home and leaving them too low when I first got her at 6 months) with which she could have hurt herself had she swallowed them. We still have a sterling hoop earring that is a mangled straight line from her early days.

She is very concerned with nipping people, and lies down and looks totally mournful if she thinks she nipped you by mistake in a game. And we brush her teeth every day. So she gets the whole "hands in the mouth aren't going to hurt me" and "I better let go immediately".
Although I do not recommend this at all, I once got her off a dog by putting my hands in her mouth in utter desperation because I knew when it clicked that my fingers were in there, she'd let go and I could get her off the other dog. I got a nice cut on one finger from that, because it took a second for her to figure out, "Oh Hell, That's My Person! "
So again, do not recommend! Don't try that one at home, kids.
But what I am getting at is that I think I could get the break stick in there. And we could practice with it in calm situations. The odd thing with pits is that once they have a hold, they just hang on. They don't keep trying for new bites--they hold what they have already. So you actually do have a shot at getting something in their mouths, even if the positioning is tricky. Their head is only moving as much as the other dog is, because they are firmly attached to the other dog. I know it sounds odd, but that's what they do. And that is definitely Jessie's MO.