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If you want more OOMP, the 7 PRC is your ticket between the 2 choices you have. And if you are looking for a gun builder, @Alex Wheeler - https://www.wheeleraccuracy.com/ is your easy button.
I'm not married to the idea of 175s by the way. I just don't know how fast the saum can push heavier projectiles. But 2900 for a 180 sounds awesome.
Fantastic question. It's the best imaginable use of a (longer) short action, at least to me… but Phil is righ: if you don't NEED to fit it into 3" then don't. you can meet your goals, or be close enough to not give a rip. In my 3" action, which is on the weaker side of things, 2650 is a moderate load for 180, 2850 is a very warm load. That's below average, but it would be a rare gun to break 2900 with 175 I'm guessing. I haven't read the thread yet, there's probably eight guys proving that wrong. Some guys get much better with different powders and actions. But it's pointless: if you know you want a saum and you are action shopping, just go longer. It's basically penalty free. That's my plan for the next one, to be able to seat the 180s and the 150 class hammers out to full length. Like you the 7prc should check so many boxes for me but for anything it actually does consistently in real life a well built saum was doing it with less drama for 20 years before. Maybe the prc feeds better, I dunno, but hysterically warning people about the saum feeding seems to be wonderfully out of fashion this year.
I talked to a guy who killed an elk with 172s at under 3" off h1000, I do not recall his MV. It was better than I expected, I remember that. But if you ask around here and on the hammer site, and spend an hour with a ballistics calculator, you might find yourself expecting better ballistics and wounding with the medium weights. Nothing wrong with the 172 afaik though of course. Just what I've absorbed. If I were building one right now I would throat it for a 180 lead and pair that with the 154-162 hammers. But a 197/172 setup? Hey why not try.
to some, if you'd like to run a short action action, Unknown Munitions makes a SA bottom metal with an XL magazine option that has an inside length of 3.150". I used it with this Lone Peak Razor SA. This rifle is actually a long throated 6.5 saum for handling 156 Berger's but I had another barrel chambered in a long throated 7 saum. I was originally going to switch back and forth but decided the heck with that and am in the process of building the 7 saum on a Lone Peak medium Fuzion. I do like the Unknown Munitions setup and have been using all 3 bottom metal lengths. For my 338 RUM and 338 Lapua imp the magazine has an inside length of 3.950 which is awesome. I use a lot of Hawkins products but in my opinion for my "hunter dbm" it's Uknown 
!. I can't offer you much help with barrel length as my are getting shorter for suppressors. That said, as we all know, if velocity is the desired outcome longer is the advantage. Good luck with your build!
I should add for what's it's worth, I personally wouldn't build a 7 saum on a long action though."Unknown"
