There are lot of good options if you "don't need the power/range of .270win " for BG.
Best choice depends on a variety f factors including shooter sensitivity to recoil, size and type of game, anticipated or required range,
Even if you "don't need" a .270 Win, it is still a pretty goo choice for many applications. One can always buy or load reduced recoil loads or just shoot normal loads if recoil is not a consideration or concern. Trust me, it won't kill anything "too dead".
That said, a short barrel, short action rifle will reduce weight. My 16.1" barreled Ruger Scout is a sweet shooter with plenty of range for most situations I've been involved in. Most, not all.
A rifle chambered for 7mm-08, 6.5 CM, .257 Roberts or even .243 would seem to fit the bill, as would a lever in .30-30, depending on the specific requirements.
But the right answer is always ".280 Rem".