I'm a huge fan of the 7MM-08 and almost always have a couple + in the safe, just in case

The last two I had built and are my favorite builds I've owned and also the most accurate where built by Shaen Rifles. I think Shaen posts here as Shooter71.
Shaen is super easy to work with and has been fantastic on his built times - always on time and as requested which is great. He also seems to do some kind of voodoo magic with his 7MM-08 builds, both mine are crazy accurate even with factory ammo.
Now to get to 6 lbs finished weight will be a little tough if you also want to be economical - not sure those go together
On both mine Shaen was able to get them both down to 5 lbs 15.5 ozs so 6 lbs is doable but you need to get the lightest weight stock you can find and then either go with a super slim contour barrel or a CF wrapped barrel which can get you there. And maybe go with Defiance AnTi action - I went with a Rebel. But you can do it and have a heck of a rifle to hunt mostly anything you will draw tags for.
Karl Feldkamp @ Kampfeld Customs is another one that is awesome like B23 posted. I have one of Karls rifles and its also a shooter. Karl is just over in Idaho and Shaen is down in California so easy to ship to either one.