I have been loading for a 338RUM, nearly identical to the 338LM. I have tried Retumbo, RL25, 7828, and 7977. Of those, I have been most pleased with 7977. It fills the case up nicely without the need to compress a 250grn bullet, and it is very clean.
I haven't tried RL26 or 33. I did get a good deal on some RL23 and was considering giving that a go, but have been so pleased with 7977 that I think I'll stick with it, notwithstanding it being a bit more expensive. I didn't start shooting 338's because I was looking for a bargain.

Demand not that events should happen as you wish; but wish them to happen as they do happen, and you will go on well. -Epictetus