As Yooper pointed out, short action MRC 1999's can handle up to 3.125" COAL. IIRC, LH Win M70 WSM actions check in right around 3.000". Both look like they should be able handle the 6.8 Western at book COAL's.
Having said that, if he is already facing having an action rebarreled, why not just re-barrel a standard long action Left Hand rifle to .270 Win with a 1:8" twist barrel to shoot the new, long, high BC, 6.8mm bullets? He can reload to his heart's content with readily available brass. Or he can be lazy and buy off the shelf ammo when it is available. Based on Hodgdon website, it looks like he would only be giving up about 100fps in MV. Other than the tighter twist rate in new factory rifles, the 6.8 Western looks like a solution in search of a problem, to me...
JMO... YMMV...