I also think that the recoil might be an issue, 140g bullets would go a long way in this gun and it should shoot the 162g bullets that you're interested in.
I'm pretty sure tha it'll have a 1-9 1/4" twist bbl, so shooting the big vld Bullets won't be a option fo you.
I found a steal on an old custom 7stw. It is built of a really old Remington 700 Action BDL platform. This spring it'll get a new stock and optics as well as a single shot follower to allow it to shoot the 180g berger vlds better. It has a 27" Sendero Taper Barrel with a Vias Brake installed as well as a pinned oversized recoil lug. I have loaded just to shoot it on paper, but no serious load development. It'll group a 160g Sierra Gameking into an inch with a generic load and 180g Bergers so far about 1 inch as well. It has a 1-9" twist,so it will stablize what is out there.
Here are a few photos:
I threw in that last one to show how pretty a 7STW bullet is. It's loaded with a 180g berger VLD, For comparision Left to right are 7stw, .30-06 AI, 6.5-06AI, .243 AI, and .243 Win.
You're on the right track for a good hunting rifle. There are times I wish my rigs were handy light weight rifles, but they are amazing at long ranges. Isn't that why were on this site???
Dan