The only thing "bigbore" about the .444 is its' bore diameter, NOT its' ballistics. It is inferior to the .405 Winchester, even! The .308 is a much better all-round rifle cartridge.

Since you like short "bullets", I recommend the .338 Federal, or the .358 Winchester. Even from a 20" barrel, with a 250-grain bullet at over 2400 FPS, the .358 is way more gun than it appears to be!