I would start with the minimum powder charge for a 300 grain bullet and work up. Try H-1000 if you have some. For reference, I shoot 90 grains of H-1000 out of my 338 rum with a 300 gr berger. My OAL is 3.670 which is important for reducing pressure and I still have a big jump to the lands.
I have used the 285 grain BARNES bullets with retumbo. 88 grains was my starting load, it was around 2600 fps, the load I ended up with was 92.5 grains, just over 2700 fps. OAL was longer than would fit in the mag, but I do not remember the exact number.