270 Winchesters are generally not 'twisted' for the long heavy bullets so accuracy may suffer. Also, cartridges based on the '06 cases require ~25% more powder than those based on the 308 case, powder charge weighs heavily in the recoil formula.
So, a 7mm-08 which is a modern day equivalent to the 7x57, may be worth a look.
Also, a clamp on brake may be worth it on any caliber. I have one on one of my Tikkas and it performs very well, great recoil reduction, ability to neutralize muzzle torque along with Tikka accuracy puts this rifle into 1"@ 109yds/100m for 10 shots. here's a link to the one I have
http://www.hss.net.au/index.php?cPath=118 it showed up in ~10 days. The Tikka is metric and so are these so there will be a size that suits.
I haven't noticed any significant increase in noise.
