for the 338 if you go with a straight taper and a shank of 1.350 for about 4-5 inches and then taper down, that allows one rechamber later on.
That is going to make a heavy blank in the 8-10 lb range with a 30-32" blank
Now go smaller shank and more radical tapers, you can cut weight.
Here is a link for pics of mine with a more radical taper
Snake 2- 338 Lapua Ack Imp
Figure stock is 4-5 lbs, and action 2-4 lbs with bottom metal
That is putting you in the 14-18 lb range with no scope
Joel Russos A5Ls are great stocks.
Manners makes some very good stocks that can be made lighter also.