Andrew: I saw this on another forum, and agree with those posters, in that the 7mmSAUM caliber is about dead. No good reason, but I believe the 270 and the 7mm WSM stole the show due to slightly better case capacity/velocities. Remington still chambers their Model Seven in the caliber, but I don't know of anyone else.
If you really have to have a seven short mag, sounds like you need to look at the 7mm WSM, or just build a nice 7mm-08 Ackley, which is what I did. Same excellent bullet selection, shorter, lighter (true short action), less muzzle blast, better handling, shorter barrel, more magazine capacity, no belt so headspaces on the shoulder properly, very accurate, plentiful brass supply (even Lapua), probably more accurate being based on the .308 Win case, etc, etc. You get the idea. Any game animal inside of 600 yards is in deep trouble with this caliber. My good friend Darrell Holland, the Riflesmith has taken coyotes, antelope, mulies, and large bull elk with his, many in excess of 400 yards, some past 600. I know him, I know this to be true. You don't need a magnum to take any game animal in the lower 48, and your shoulder will thank you, as well as your ears.....
Here's a 120gr Nosler BT WS2 coated in the mag well of my PGW Model 15Ti in 7mm-08 Ackley to give you an idea of scale:
Compared to a .270 Win with 130gr Nosler BT/7mm 120gr Nosler BT:
There has been much written on this caliber by some very experienced writers/hunters/shooters. You may want to look into this prior to any 7mm build.... Just something to consider in the Grand Scheme of Things.......