If the bullet is stable at 500 yards, it will be stable further out as well, more and more stable in fact. This doesn't mean it will be stable through the transonic range, but any stabilized bullet has no guarantee it will either. When the temp drops you may run into a problem if it's borderline stabilized.
Kirby,
What temp and pressure have you tested them in the 10 twist barrel at?
It would be interesting to know (but take more than a few bullets to find out) if you ever slow those bullets down, at what speed they finally go unstable. Seems that the 10 twist might be borderline enough that reducing the speed to 2900 fps or this could begin to happen, maybe.
What's the length of the 350 gr, Kirby?