You should be just fun here, but Berger's recommendations are usually pretty good about what these bullets will or will not do in re stabilization. Give it a try, but I doubt you'll see any problems at all here.
I don't have a STW but I have a 284 Win with a 1-9" twist 29.5" barrel and shoot the 180 Bergers at 2870 fps, they stabilize fine out to 1000yds, I shot a 6.1875" 5 shot group with it today in windy conditions.
I think they will shoot just fine out of your STW.
Wayne aka WAMBO
Decided not to try the 180's. After running ballistic software the 180's under
perform the 168gr.
168gr Berger @ 3125FPS 20.25 MOA @ 1000yards w/ 1265# energy
180gr Berger @ 2950FPS(est) 22.25 MOA @ 1000yds.w/1264# energy