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.
Remington Managed-Recoil Cartridges
Winchester 100 .243; Marlin XS7 .308; Stevens 200 .223; Rossi 92 .45LC; Marlin 1894C .357M; Marlin 30AS .30-30; NEF Pardner Pump 12ga; Mossberg 500 Turkey 20ga; Winchester 1200 20ga; Savage Mark II F .22LR; Henry H001 .22LR; Marlin 60SB .22LR; Ruger 10/22 DSP .22LR; Browning SA-22 .22LR; Savage 93R17 GV .17HMR; Remington Genesis .50 cal ML; Ruger SR1911 .45ACP; Ruger Vaquero .45LC; Ruger Blackhawk .357M; Ruger SR9c 9mm; Ruger Single-Six .22LR; Browning Buck Mark Camper .22LR