I have owned and worked with many 338 Lapua's . My favorite load would be Lapua brass, CCI 250 Primer, H-1000 and a 300 gr Berger either the OTM or the Elite Hunter. This should be a great combination for your 1 in 9.3 twist. Start about 88 gr and look for pressure to start to show between 90 and 92.5 gr. Seating depths with the 300 Berger have been easy for me. Most come in between .005" and .060" off the lands. Many like .015" off the lands.
The difference between the OTM and the EH is minimal and consists of the EH having a slightly thinner jacket to aid expansion. But I doubt you can tell the difference in terminal performance until you go way beyond where most of will take a shot on elk. I do recommend that all bullets used for hunting are checked for tip blockage. Use a stick pin, paper staple or I use a wire drill .027" or a little less and check to make sure the hollow point tip is open back in about .300 of an inch. Sometimes tips get clogged with jacket material during production or our loading process and this will greatly reduce expansion if clogged.
We have taken elk for years now with the 300 OTM now. Many years in the 8 to 10 range. I have lost count of how many total. But I don't remember one needing a second shot and we have not tracked one from the immediate area. Our placement of choice is in the crease tight behind the shoulder a little below center.
Best of luck to you
Jeff