I did this twice with two custom shop guns. One is a 270 WSM out of the Weatherby CS, the other is on a 700 Rem action made by Red Hawk Rifles in Grand Junction Colorado. That is a 30-06. Hands down if I were to do it again I would have built two with Red Hawk. The quality is superior to just about anything else I have shot. For about $2200 I have a blue printed action, cryogenically traded fluted barrel, with a Timney trigger in it. The bolt is spiraled, the bolt handle is skeletonized. The metal is all black oxide finished. Stock is a B&C medalist. I put a Monarch UCC 3-10 by 40 with Leuplod B&R. It shoots .25 all day long with Nosler 150 gr and RL19. I have taken many deer with it. What I wanted was a lightweight rifle in a 30-06. What RHR gave me was something I never would have imagined owning at 6.5 pounds.
There are two other custom builders that I would look at as well. Hillbilly Rifles in Vermont and Dixie Precision in MS. Both are making very fine custom guns for not much more than you would buy an off the shelf Mk V for.