I've seen some really bad all season/ all terrain tires with snowflakes on them, and good ones without, the LTX MS is definitely a tire that should not get the flake. It's a hard compound long life tire, and is poor in winter conditions even though generously siped. OP, if you drive in water, then hit a dry patch, do the rears give you a full print. I ran 265/75-16's in the same tire on a super duty crew cab, I had full print at 55psi on the front, but even at 45psi I didn't get a full print on the rear, I believe 40psi empty was the magic #, I'd drop a hair more, it could make a slight enough of a difference to make it predictable, maybe not perfect but better. I really like the tire, but it needs a bit of finess to get it to work.
The GM at the local tire shop tried a set when they first came out on a 3/4 ton Ford, 235/85-16's, even loaded with 16-20ply rig tires it sucked on icy roads, Michelin told him to keep dropping psi to make more traction, he stopped once he got into the 20's and just put on some winter tires. It did get better but just not good enough. Might be the same situation here, 2wd high torque diesel, no weight in the rear, dropping a bit more pressure should help, but I wouldn't expect a drastic change. I wouldn't change out the tire, a softer compound tire may help in the wet, but now you're going to have a tire that will burn off in the dry.
Drop down to 38-40psi, see what happens.