Since you dig the shorter cartridges...,

300 WSM, .325 WSM, .338 RCM, .375 Ruger,


I would have added the .338 federal, but you already have a .308, and a .444 which you have, big, heavy/slow covered, I'd get something with some weight and range to it....so kinda a short mag.....the ruger is still long, but shorter than the H&H, and you can get one in a short rifle/short barrel, and with it being a 375 you can still get some performance from that shorter barrel.