The MDT LSS is nice and light. With a shorter barrel you might get the bench accuracy you want with enough weight savings to hunt with it.
I have also owned a KRG Bravo, and while its very nice, comfortable and affordable, it was a bit heavier than the LSS.
At one point I had 2 heavy barreled 700s in both chassis (26" and 24") and I'd say they could both be a bit much for hunting. I suspect a 700 sps tactical or something similar with a 20" heavy bbl might be do-able. Its the barrel weight that is the biggest problem. Even my stock 700 sps 26" with the tupperware stock would be too heavy for hunting, for me anyway.
The LSS is available for many rifles such as the 700, savage, tikka, ruger american to name a few.