This a 22 page thread about the Rem 700 P in 338 LM. Scattered through the thread are posts about powders, bullets, and brass. An unscientific guess at popularity based on that thread:
powders; H-1000 and Retumbo
Bullet type is always a long conversation but some guys are having excellent exterior and terminal ballistic results with VLDs in 250 and 300 grain.
Here's the thread;
Remington 700 Police 338 Lapua rifles - Sniper's Hide Forums
Hope this gives you a starting place.