I agree that you want a longer tube. At least 26, but 28" would be better. 7mm RSAUM is pretty overbore and needs room to work. You can make it happen in a 24" barrel, but a straight .284 Shehane will give very close velocities (within 100fps) and much better barrel life, if you want to run 24" and not push the gun that hard. Using 5-7gr less powder and getting only 50-100fps less is a big win-win in my book...
In any case, 180 Bergers are THE bullet, hands-down. Load them to max mag length and get your barrel throated just a little shorter, so you can load them out as the throat burns out (which is gonna happen fairly quickly with 7-RSAUM).
Best velocity will come with a compressed load of something slow, like RL25, H1000, or maybe even Retumbo. Mag length will affect powder selection, because if you need to load those long 180's to something near the SAAMI OAL spec, you aren't going to have much case capacity to work with. If you can load them way out (say, using a Savage, or a long-action), then you will be able to use those slow powders. 60-62gr is about where you'll end up, if it fits... start lower, of course.
I like RL17 for the Short Mags with heavy bullets. It's much easier to get than the Hodgdon powders. If you can get a steady supply of H4350, that's on the faster burn rate (slower velocity) side, and will work fairly well without large charges. I would start no higher than 50gr for either powder. H4831sc is in the middle and possibly a good all-around choice, again - if you can get it. I'd start around 55gr with that - max is over 60 for most guns.
I know those load recipes are vague, but short mag pressures vary dramatically based on seating depth. A 7mm-RSAUM with 180gr Berger loaded to fit a factory Remington mag is practically a different cartridge than one loaded out. I got over 250fps more from 300WSM than 300RSAUM, with the same length barrel... because the WSM was a Savage that let me seat heavy bullets way out there. The RSAUM was an R700 that made me feel like I was pushing 200gr+ bullets right up against the flash hole.