mw,
A few years ago, I bought a Savage in 270 Win for my Son-in-Law, who at the time was on a military deployment. He's shorter than you with a relatively short arm reach. When I received the rifle, I quickly realized the issue you're facing. Even though I am taller than my Son-in-Law, I had trouble getting a mount and scope with enough eye relief to suit me. Trust me, I checked numerous options for about a month straight. I finally arrived at a solution with which my Son-in-Law is extremely pleased. It works for him, even with his bulky hunting clothes on.
I had the stock cut (LOP reduced by 1" including a Sims Recoil Pad installed). I installed a Warne 1-piece tactical base ("0" MOA) and mounted a Leupold 6 x 36 scope, which has a little over 4" of eye relief. I had initially used the Warne QD rings with the levers but I noticed that accuracy started to deteriorate the more I shot the rifle. Thinking that the rings were the culprit, I then installed the TPS Product tactical rings (TSR steel rings), which are mil-spec picatinny (as is the Warne tactical base). Presto, this rifle is now a tack driver with just about anything I feed it. When recently testing 7 boxes of different factory ammo (I obviously do not reload for the 270 Win), 6 out of the 7 factory offerings were very accurate at 100 yards.
A few things to note about my arrangement of which you should be aware: 1) At that time all Warne had available in 1-pc tactical base for the Savage LA was blued steel. Since the rifle is SS, there is a definite contrast, which we both like. This may not apply to you but I thought I'd mention it; 2) My SIL's Savage has a detachable magazine. So, the 1-pc base does not pose any loading/unloading hassles; and, 3) I bought the Leupold scope before I decided on the mount. I'm fairly sure that I'm not restricted solely to long eye relief scopes for this rifle but I really have not tried such a scope. So, I can't say for sure.
The above set-up is what worked for me and my SIL, after much research and experimentation. It may or may not work for you. I just wanted to give you my $.02 worth. Good luck.