I think it's 284, 7x57, or a 280 with the unknown munitions DBM (if that setup really will feed a 3.45+coal, I have never seen one.)
My thinking is for the price of the Unknown Munitions DBM and two mags is that you can probably find a .532 bolt (or a donor rifle) and go WSM, either 300 or 7.
Downside of the 300 WSM being recoil with the weight of bullets you'd need to hang with the 7 (as someone else has already mentioned). But the WSM will hang. In one of my WSMS I run 212 ELDX's in a standard throat @2.95.
Or do a 7WSM. Basically the powder capacity as a 7PRC. Downside of the 7WSM being you are stuck with Hornady brass or sometimes finding big lots of Winchester and sorting it. But the Hornady brass is fine as long as you buy a few boxes of the same lot and do some minor culling.
My 21" 7 WSM runs 180 ELDMs at 2850 and that is limited by a 3.00 COAL. You'd probably get another 100 fps from a 24", more if you could throat it for a long COAL.
Anyway...maybe a bit off track...but sort of a question of how married you are to 30-06 bolt face when you're already dropping the cash on a barrel and getting it chambered.
EDIT: again, not that you asked, but a 7WSM with a 180 ELDM seated so the boattail is just below the shoulder/neck junction is 3.20". The case holds a sh*tload of powder. Throated appropriately, with a 24" barrel, you'd be over 3,000 fps with 180 ELDMs or at least have enough wiggle room to find a node around there.
Anyway...I'll shut up.