Don't take this the wrong way, but I'm afraid you're considering a fool's errand here.
I've owned two LWStorms now. Still have one. Rebarreled a long action LWS to '06 in fact (from .270) with a standard sporter weight stainless '06 Savage barrel. Took it elk hunting even.
The greatest weight savings in the LWS is from the barrel. That 20" barrel is pencil-thin and weighs less than 2 lbs. Not sure there is any way to thread one, they are so thin at the muzzle (.560" I think).
As for the round, in a 16" barrel you're better off with a .308. You'd never burn all the powder from an '06 in a 16" barrel, I don't think.
I have a real fondness for those LW Storms now though. Fantastic stock, even though they don't have the adjustable cheek risers. They fit me better than any stock I've ever owned, and that's a lot of stocks.
To answer your final question, the weight savings from the receiver and bolt on the LWS is only about 1.5 oz. total. That's it. The rest is in the barrel, which is about 8-10 oz. lighter than a standard 22" sporter weight barrel.
My advice would be to buy a short action LWS and rebarrel it to a carbon fiber 16" .308 that's already threaded, then run the can on it. You won't get any lighter than that and you'll get better performance in the long run.
In a 22" barrel there is only about 100 fps difference between the .308 and '06 and in a 16" barrel it will be even less. IOW - not enough to matter.
Best of luck.
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