There are bolt face differences with this conversion also. The 356 is a rimmed round while the 35 rem is a rimless cartridge with a considerably small case head and bolt face. That's the only distiction between bolts for the 336 series rifles. The 375 and 444, 45/70 are different enough they get seperate listings.. Still so many of thesee rifles have been made parts availability is not a problem..
I thought about this for a couple of days(be afraid, very afraid) and the simplest fix would be to simply rechamber and use 358Win brass. These are the same rounds with different case heads.. They are also loaded to differing pressures I would imagine but really don't know. You wouldn't be able to use pointed bullets but then a 356/358 isn't a long range rifle anyway.. I bought a 760 remington in 35 remington for just such a project.. I also bought a junker of a 760 a few months back in 30-06 to rebarrel to a 35 Whelen.. Lot of 35's all of a sudden!