I have a Ruger American compact in 7mm08 that comes in well under 6lbs. Here in the next few months the barrel will get fluted and threaded along with whatever metal the smith can shave off the bolt and receiver to cut as much weight as possible. The gun cost me under 400 bucks and shoots 1 MOA with Nosler trophy grade140gr accubonds all day. All in I'll have a close to 5lb bare rifle that didnt break the bank.
What length is your barrel, or will it be when it gets back from the smith? Do you have a specific thread or post on this rifle? If not, you should start one. I’d be curious to know how this turns out and what the end weight will officially be, as well as how it shoots and handles. Keep us (or at least me) posted.