Seating depth in guns having magazines, is always controlled by the magazine length.Besides the short mag box in the Winchester model 70 I've had good luck with 150 eld x and IMR 7828ssc.
Unless of coarse you opt to just single feed it.
I use 162 gr Hornadys in my 7x300 wby on a standard 700 bdl action with seating depth so they fit into the standard magazine. It only holds 2 plus the one in the chamber, but the deeper seating depth does not have a noticeable affect on the accuracy. Again, the 7x300 wby and the 7stw are balisticly clones.
7828 is the powder to use in my opinion, 3400 fps with the 162 isnt unheard of.