You left out the left handed shooter part. With that being said, I would work with the .270 you already have. It's a great hunting round. Like others have stated, try a better recoil pad and/or managed recoil cartridges. 130gr will produce less felt recoil than 150gr, but not that much.
I'd suggest getting a soft rubber recoil butt pad fitted by a gunsmith, I'd done that with a 30-06 Savage 110 with very excellent results I'd done mine myself but had help and it looks allot like the top picture but mine has a very soft, almost jelly like feel to it, it tamed the monster, another thing is getting one those kenetic recoil absorbers installed if the rubber pad isn't enuf they are inletted into the buttstock and held in place by the recoilpad. PRE-FIT RECOIL PADS - Brownells