I have the slightly larger case, a 7mm/375 without the shoulder moved back like the LRM. I tried H-1000, US 869, Retumbo and RL-33 with 168 Berger hybrids. Didn't bother with the 180s because the rem 7 mag takeoff I rechambered is a 1 in 9.25 twist. The rifle really came alive with higher velocities and good accuracy with RL-33. With a 26" barrel and 86 gr of RL-33 I am getting 3268 fps.
Obviously your LRM will use less RL-33. I would start with a charge weight a few grains below the top load for Retumbo and work up from there. This approach has worked for a 6mm-284, 257 Weatherby, 300 RUM as well. Alliant may have made RL-33 but their load data is very limited.
Ramshot Magnum might be worth a shot. My LRM shoots lights out with 71.6 of H1000 and 180 Hybrids so I am not messing with it anymore. I am getting just a touch of smoke on the necks so I am already on the slow end with H1000.