Like most things in life moderation is the key, everything is a trade off. This said, your parameters aren’t unreasonable (short barrel, 300-400 yards max). I also like short barrels, and have spent a lot of time on short barreled builds and rifles, trimming down to that from highs of 29” to a contemporary preference of 18.5-20”. Make a short list of cartridges, and google “Rifleshooter, Ballistics by the Inch” and the cartridge. They’ve done most of them, cutting barrels back and chrono’ing velocities as they go.
Few points to keep in mind to help the decision process,
-Muzzle blast starts to get obnoxious under 22” in a standard magnum (7mm, .300), and truly obnoxious by 20”. Nothing hearing protection can’t deal with, but it’s a major increase over a 24” in a .300 etc, and you’re never going to want to take a hunting shot unprotected. This said if the rifle is a hunting rifle and carried more than shot, the short barrel can be a reasonable trade off for the ease of handling.
-In the spirit of moderation, moderate cartridges like Hoyt’s .358s or even plain old .308 see less velocity loss in short barrels. Todd’s quickload proves out that large capacity cases remain faster in a shorter barrel, there’s no getting around physics, powder is available energy and energy equals power. However with a .358 you may see as low as an average 15-20fps per inch loss of velocity for every inch shorter. A 7 mag may 40 fps per inch, or 200% or more velocity loss per inch. Statistics and twisting them to make a splash is fun.
-Medium and larger bores (.338, .358, 9.3, .375, .416, .458) are affected less than smaller bores by barrel length due to expansion ratio. The burning powder has more volume to fill in a larger bore before the bullet leaves the barrel, allowing more work to be done before the bullet’s sent on its way. Like everything else, compromises are to be made, I wouldn’t choose a .458 for 300-400 yards but it can be done.
-Most good ideas have already been done, there’s a reason short .308s abound and short 7 Mags get looked at like a three winged chicken, I wouldn’t try to buck convention too hard lest disappointment result. Usually that disappointment comes in the learning to live with it factor (muzzle blast, recoil) rather than the gun’s actual capabilities.
In summary, for what you want short barrels, as short as 16” and 300-400 yards range, I’d suggest it’s hard to argue with a 16-18.5” .308 Winchester. Again I recommend reading the “Ballistics by the Inch” on it. I’m building a new .308 right now, and it will likely have a 20” barrel just my preference in an agglomeration of compromises, but it won’t do anything different in the field than a 16”.