First if you can't shoot it with absolute confidence and accuracy no cartridge will work. So I will list a few and pick from them what you can shoot effectively. 375h&h, 338win, 35whelen, and 45-70+p. The whelen with 250gr partitions will work out to 250 yards with recoilless than your 7mm rem with 175gr bullets it willbe in a slightly lighterrifle and have a bigger heavier bullet. Same for the 45-70 in a 1895 marlin but more recoil. The 338win isa great choice butit comes with recoil and weight.

Remember felt recoil has everything to do with velocity not so much as bullet weight, but penitration dose have everything to do bullet weight and less to do with velocity
I personaly do not like the recoil of the 7mm remso I have a 35whelen for the big stuff mainly elk/moose but it works great on browns tooand a 270win for deer toelk/moose.