Tricky situation.

If your balls are getting significant scratches in the track area in 9-12 games, that, to me, is a good sign, that the lanes you are bowling on are in really bad shape (old and worn). I assume it's a league, so I can't suggest not bowling there. If it isn't a league, well, don't. Especially, don't practice there.

If you have less  ... valuable balls, use those in this place, if that's an option.

If the ball is polished, try to polish only the track area, as the rest of the ball is not being affected. If the ball is dull, sanding removes shell and you should really sand the entire surface as evenly as possible to keep the ball in good shape (but, that, of course is obvious). So I wouldn't sand the ball until it is obvious that the scratches are affecting the ball's reaciton.

I think your only two options are either not bowling there or use less valuable balls, if that is an option. If not, I don't see any alternatives.

Much of this is obvious, but sometimes putting it in words helps clarify the situation in your mind. It is possible that I missed one or more alternatives. Good luck.
--------------------
"None are so blind as those who will not see."