It would make sense to me to chamber it into 5.56 NATO instead of 7.62 x 51. The latter would seem a little overdone. First, the rounds are more expensive. Then, if you want the range (distance), there are more appropriate rifles to handle that.
I've also heard that the action isn't that reliable in its native 7.62 x 39, so how would it handle a much more powerful round? Would the action be more prone to stoppage or breakdown with the harder recoil?