I started a similar project to build a multi-use 375 that was not too heavy, my previous 375 weighed about 10.5 with scope, and around 9.25 without.
I found that many of the Win Alaskans can be had at around 7.5 to 8 pounds, but not all. They need to be weighed. Anyway, I finally found one that I could weigh and it came in just under 7.4 pounds.
My initial goal was to hit 9.25 pounds with scope, bases etc. Then I got a little greedy and wanted to hit 8.5-8.75 pounds.
Then I got a little scared
So decided 8.75 or a bit more was probably the better part of discretion over valor.
Long and short, even with a bigger-than-I-intended scope and some extra length of pull, mine weighs in at 9lbs even, with the standard wood stock.
So it can definitely be done, probably even lighter if you go synthetic. But I don't think I am up to that level of recoil, and I love wood!