First of all I have no experience with the .260 Rem. However I have modified several rifles from the Savage lineup. Most come with a 13.5" LOP and the recoil pad is around 1" thick, so instead of cutting down the stock fit them with a new 1/2" recoil pad and you are right at 13" LOP. That said I'd have no remorse about cutting down a Savage stock, they don't use the highest quality walnut in the first place anyway.
I don't get the see-thru mount comment? I'd say your shooting technique needs a little work, or you shoot some very ill fitting rifles if you are having problems getting the scope to line up. Straight stocks usually are better for eye to scope alignment than a stock that drops a lot to the heel, as those are usually better for shooting iron sights. I find that see-thrus are a terrible mounting system. Remember you bring the scope up to the eye, not the eye down to the scope. You'll be more comfortable and shoot better in the long run.