Suggest you identify the appropriate projectile first based on your application, and the twist rate of the rifle.
For example, Berger Elite Hunters may be a good choice for hunting, but does the twist rate support 300gr or would a lighter projectile be more appropriate.
Next, measure your chamber to determine seating depth. Many of my rifles like 10-thou of jump to the lands. Beware potential pressure spikes seating on the lands or jamming.
Are you using Lapua brass? New? 1F? Did you prep the brass or just take it from the box and shoot it? Sometimes the necks get dinged in transport so they're not perfectly round.
Also, what setup are you using? Single stage press? Brand of dies? Are you measuring seating depth with a comparator, etc?
Select propellent - H1000, US869 seem to be pretty common for .338 LM.
Start low and work up...keep us posted on progress!