"...since money is so tight..." If money is tight, not entirely unusual, forget about it. It's not inexpensive. The barrel alone can run $300 or more plus installation.
"...If I weren't left handed...definitely pick up a used military rifle..." Never been an issue for me. Mind you, I'm more interested in shooting the rifle than anything else. I don't care what the calibre or cartridge is. If I buy it, I also buy dies, a shell holder and as much brass as I can. A bolt action battle rifle won't help your back. A CMP M1 rifle, shouldn't though. Gas operated .30-06.
"...how much could recoil be reduced..." Depends on the cartridge. Using a lighter bullet makes a difference.
"...reduced recoil 7 mm loads..." They won't necesarily shoot well out of your rifle. Sell the 7mm Rem Mag. Too much felt recoil and seriously overrated as a hunting cartridge. No game requires a magnum of any kind. A .243 will kill deer with no fuss. Felt recoil is relatively light and you can get one in a semi-auto. Semi-auto's have less felt recoil than any other action.
Talk to your MD first though.