I mark a big X where the hinge is and leave that area alone. Remove wood from above and below. Retiller the other limb.
To prevent hinges don't use power tools for final tiller. Once I string it, I'm using a scraper like tool. Also, remove wood in long strokes going past the target area by a little. In addition, take your time. No hurry. Check tiller frequently. Work thewood in with a few partial draws.
Jawge