165 / 168 Gr. Barnes bullets are pretty popular with 300 mag shooters too... the 180s are pretty long and tend to take up powder capacity. I'm not sure if you've shot Barnes bullets before, but they give really good penetration and a guy can go down a bullet weight and get the same performance as a heavier bullet.
#4 manual doesn't show anything for any of the 4831's. We use RL19 in both the WSM and the Win Mag for 150's and 165's. As posted you can drop a bit of bullet weight due to the penetration of the Barnes plus the WSM's a tad short anyway for a pretty long bullet like the 180 TSX. 4831's might be a tad on the slow (burn rate) side for the WSM.
H 4831 might be a tad on the slow side, your apt to run out of case capacity before getting close to published velocities. Try some IMR or H4350, IMR 4831, or even some RL19.