A new rifle in 6.8 makes more sense. The parent case for the 6.8 is reportedly the old .30 Remington case. The rim diameter is 0.422 and the case length is 1.686. The .270 Win. rim diameter is .473 and the case length is 2.540. Plus the .270 case has a fatter body. Sounds like a tough conversion, but the gunsmith and barrel maker might be able to pay for Christmas with the proceeds. I think it is one of those conversions where you keep the butt plate and start over.
http://www.remington.com/products/firearms/centerfire_rifles/model_700/model_700_SPS_specs.asp6.8 Rem SPC 3 26" 9" 46 1/2" 7 3/8 27371 $559
I doubt if a lot of firearm manufactures are lining up to chamber rifles in the 6.8 round at this point. You might find a few AR manufactures that are chambering for the 6.8 Remington and you will find them rather pricey, but the recoil should be reduced.
Remington also sells a Managed recoil load for the .270 Winchester loaded with a 115 gr. C-L bullet.
I did some checking on some bullets and found a number of 6.8/270 bullets of interest.
Remington Core-Lokt Ultra Bonded Bullets 6.8mm Remington SPC (277 Diameter) 115 Grain Pointed Soft Point Box of 50
Barnes Triple-Shock X-Bullets 6.8mm Remington SPC (277 Diameter) 110 Grain Boat Tail Box of 50
Sierra Pro-Hunter Bullets 270 Caliber (277 Diameter) 110 Grain Spitzer Box of 100
The traditional, flat base design of the Pro-Hunter has been skillfully blended with Sierra's world-famous accuracy. The custom-tapered Pro-Hunter jacket design helps assure maximum expansion, optimum weight retention and deep penetration for game-stopping, 1-shot performance.
I did not list the Hornady 110 bullet because they say it is a varmint bullet.
Looks like there are a number of good bullets designed to work a low velocity on deer size game in the .270 Winchester.
Another option is CAST bullets. Either cast them yourself or find a source. As an example Lymans #280412 bullet will give you about 1445 fps using 13.5 grains of Unique. The load produces about 2-pounds of recoil.