Haha.... Oh boy nagant... Can't say I will have the ability to go down that road any time soon. I have three babies (>8yrs old) with a fourth due any day now and meat in the freezer is money not spent at the grocery store. We're not poor, but funds need to be spent wisely.
The weight restriction Rich include scope. I have a 4x scope that weighs 8oz with rings but I could also save for a 2.5x Leupold that weighs 6oz.
I was thinking compact rifle (17-20 inches) in either a bolt action or lever. Single shot rifles don't weigh much different for some strange reason. There's a guy I heard about (can't think of the name right now) who modifies Marlin 336 and Win 94's to weigh ~6lb. If I snag a 30/30 and go 32 Special or 375 Win by JES, his rebore will actually remove metal inside the barrel, reducing weight further.