I don't know where your custom Rem LSS Mtn rifle will come in weight wise but the factory version is about 6 1/2 Lbs. I can't even begin to imagine the recoil of a 350 Win Mag in a 6 1/2 Lb Mtn rifle! Hope you're not recoil sensitive.
Actually I own a .350 mag Custom KS Model 7 from the remington custom shop. It has a 20"BBL and Macmillan Synthetic stock and weighs under 6 lbs without scope and as much as people rant that it would be brutal to shoot it is not at all. Very similar to a stout 3006 load. The problem with the remington model 7 action is that its length limits the amount of bullets you can use with the .350. For that reason if I was building an elk and moose rifle on that action and didn't want a .35 cal I would opt for a .308 win. With 180 gr. Partitions cranked tp 2700 fps its no different than a 3006.