As a guy that put a Bartlein CF barrel on his M70, I'm certainly not going to tell you don't do it. I'm just hear to remind you that if you want to save weight, buy a steel barrel. Take the money you saved on the barrel and buy a custom action and a lightweight optic. If I had it to do all over again...
Right now, I'm about (math...$1350 base, $1000 for barrel, chambering, cerkote, $250 trigger, $660 on stock w/ .mil discount) $3250 and some change. I easily could have had a custom action for less than the base rifle price - lesson learned on that. Speaking of, that's not much less than my KRG SOTIC ran me with intro pricing. If I wanted a custom action on a budget, the Mack Bros over a worked Remy would be the easiest non-decision I'd ever make.
If I just wanted a hunting rig and a 13.125" LOP was G2G - Seekins all day. Guaranteed to be lighter than my 9.5 lb custom rig with CF everything and likely to shoot every bit as well. If Seekins would make me a 12.5" or 12.75" LOP stock they'd already have my money...I think about the Havak Element every day anyhow, heh.
Alternatively, you can do what I did and buy a Tikka T3x project rifle in 7mm RM. I got one here on the Hide for $600 or so - all I really wanted was the action, but it shoots well enough that I've kept the factory tube for now. PROOF makes Tikka factory contours and CF prefits. You could be on the range with about $2k into the rifle (assuming you spend about what I did on a custom stock) if you shop around a bit.