If you go 7WSM / 7x300WSM / 7x270WSM you need to look at something that is long throated to maximize case capacity. Even so you are going to be hard-pressed to find 3,000 fps in a 26" tube with a 180 Berger. My 7WSM is long-throated (to over 3.1" COAL) and I could only get the 2,900 fps node in my 26" tube. If you bump up to 28" you might get there, but maybe not depending upon where you are located. My long-throated single feed only F-Class 7WSM hits 3,000+ but its got a 30" tube on it.
I don't think the SAUM can do it but with some newer powders maybe (I am skeptical w/ the 26" tube).
If you go 7LRM or 7 Rogue (or whatever else they are calling a 300Win Mag necked down to 7mm) you can get there w/ a 26" tube.
My 7 Dakota hits 3,200 fps at its high pressure node and runs @ 3,100 all day long (but its a 29" tube). Cut to 26" it probably gives you 3,000 fps.
I'm not a recoil weenie by any stretch, but all of these will thump you a bit even with a fairly heavy rifle. None of my rigs wear a muzzle break (but none is lighter than 17 pounds). I've run my 18 lb 7 Dakota in F-Class using a bipod. By the time I get to the 50-55th round I'm focused as much on recoil management as I am on shooting for a score. Same for my 17 lb 7WSM - by shot 65 or so in 3-4 hours you want it to be over. If we are talking 10-15 shots its not going to pose a problem at all (at least for me).
convert one of these rigs to an 8 lb pure hunting rig and she will thump you for sure. Doable absolutely, but not for extended range / desert / plinking shooting adventures (at least by me).
Jeffvn