Note a couple things on the loads for my Tolley.

For one, there are two different charges engraved on my rifle -- 4-1/2 drams and 5-1/2 drams.

Also, the cartridge that it's built around was *either* a 270gr tubed bullet or a 360gr soft. My guess is that it would work well with either period load.

I've worked with some bullets lighter than the 350, although not anything as light as a 270gr, as the rifle didn't like 300gr softs, and I couldn't find a 270gr with the same length of an original 270gr tubed bullet -- which were long for their weight.

I also have worked with 4198, but ditched it as the Varget load was much more accurate.
Note that my good load includes 21 grains of dacron.
Cases for the rifle discussed here would likely take less, but the point is that it takes quite a bit to fill the case so it's packed firmly. Weigh out 21 grains of dacron as an example to get a sense of how much fiber I'm talking about.

Good success to you with your load development.
My recommendation is to start with Varget and the Hornady #4502 350gr SNRN bullet (that's if your grooves are .458"). Don't use the current Woodleigh 350gr SNRN as it's designed for use in the 458WM and has a harder core and thicker, harder jacket than the Hornady.
Woodleigh has discontinued their 350gr SNRN for the BPE rifles, and that bullet had gotten great praise for this kind of load, but they're gone and the replacement is too tough for these barrels. Careful with that one.

Cheers
Tinker