I shoot a Ruger #1 International (20" barrel, Mannlicher style stock) in 7x57 and, YES, the shorter-than-24-inch-barrels won't give quite the muzzle velocity of the longer barreled rifles, BUT... getting 2800 fps or close to it out of my Ruger's 20-inch barrel isn't a problem.
My hunting load (for deer) is a 140 grain bullet in front of 50.0 grains (a MAXIMUM "published" LOAD)
of H4350 sparked by a standard Winchester large rifle primer in Remington cartridge cases.
There are a good many different 140 grain bullets available for the 7mm... and while I have always used Nosler Partition Bullets for hunting big game in .338 Win. Mag. and .300 Savage, I may end up using the flat-based Sierra 140 grain ProHunter bullet which is a very accurate, cup & core type bullet, but quite adequate for deer-size game.
For elk, I'd recommend a 160 grain or a 175 grain Nosler Partition Bullet in front of a healthy charge of H4350 powder. My Ruger #1 "loves" H4350 in any amount and has shot 3-shot groups as small as .176 inches at 50 yards using 37.2 grains of H4350... and if you want ASSURED
expansion as well as deep penetration, then use the still excellent Nosler Partition Bullet in 160 or 175 grains.
My deer hunting load (50.0 grains of H4350 & a 140 grain bullet) has shot 3-shot groups of .404 inches with a noticeably heavier (but not objectionable) recoil and a louder report... with a muzzle velocity of around 2800 fps out of it's 20-inch barrel.
Strength & Honor...