Barnes lab test show the 120TSX at 3000fps will expand at 700yds.
I wouldn't put too much faith in that claim.
In 30degF and 26.8 InHg that bullet is only traveling at less than 1600 fps at 700 yards- well under the expansion velocity rating for the 120 TSX. If approaching those impact velocities, I'd certainly feel better about the LRX than the TSX. Given your muzzle velocity and range restrictions, any of the above will expand properly, but the LRX will drift slightly less in the wind. Out to 500, there's really not enough of a difference to worry about.