I have had a 375-06 for the last 8 years now. I know this isn't exactly for 300 grain bullets, but I have been using IMR 4320, 60 grains with the nosler 260 accubond gives me 2600 fps out of a 24 inch barrel. I have found about the same amount of RL 15 gives me the same velocity the 4320 was just more accurate.
Good luck I'll use my 375-06 for anything with the Leupold CDS dial I can take it all the way out to 600 yards.