Edit - rethinking my post here.
Seems that I recall a 6x39 wildcat already exists. I think a 6.5x39 does too... just don't know about that one.
If you necked it properly, you could have enough shoulder to headspace but the problem is the lack of powder capacity. You may be better served by starting with .308 / .30-06 brass and opening up your bolt face to use the .308 round.
Found my pic of the Grendel vs. 6mm PPC rounds: