Can you post some pics? I have considered looking at a wildcat based on a shortened 308 necked to 338 to what-ever length case could still seat a VLD 338 bullet and cycle in a normal short action magazine (AR-10, FAL, M14, BoltGun).
I am guessing that this would be very similar to what you are doing or perhaps a little longer case...
Here is your 7mmBR case:
compared to the 308...