I've owned a few over the years , I just traded a Ruger M 77 in 350 RM for a Marlin 45/70 . It's a great round , but is a bit of a kicker with heavier bullets . Add that to the fact that there weren't a lot of rifles chambered for it and limited ammo availability pretty much explains it's lack of popularity . My brother has used the same rifle in 350 RM for over thirty years , A REM Model 700 , to take more animals than I can remember. He's always used 250 gr bullets loaded to about 2400 fps on everything , as far as I can remember, he's never needed more than one shot . I used the Nosler 225 gr partitions along with Hornady 250 gr SP's , both worked perfectly on moose , elk and deer . The 225 do give a bit more range than the 250's and , in my experience , don't give up any penetration or " knock down " ability to the heavier bullet .
That being said , my next 35 will probably be a 35 Whelen . It's a lot easier to form your own brass , trust me I had to make my own 350 brass when Remington dropped production a while back . They have resumed production , but I won't be surprised when they drop it again . Ballistically , they're identical , and I can fit four rounds in a magazine with the Whelen . Other than that , I'd use either round on anything in this part of the world with complete confidence . I hope this helps , but if you do decide on one , you won't be disappointed with it's performance on game .
A2