Like Roy above I have a 375 Allen Mag which is an improved version of the 375 CT. My rifle weighs 17.5 lbs with a NF scope. The rifle is in the $5k ballpark without bells and whistles.
TAC 408 single shot. 1.60" $1100
McMillan A5. $800
Lilja Allen 32 31" barrel. $485
NF ultralight rings. $170
Jewell trigger btm safety. $230
Allen 5 port painkiller brake. $250
Over $3000 just in componets W/O scope which is $2k plus. There is no sense in building a rifle with the capability of the 375 CT and not putting high end optics on it.
IMO if you are going to try to build a bare bones or budget rifle the cartridge you have chosen does not lend itself to that kind of build. These big guns are expensive in all aspects especially shooting. The 350 SMKs are gone. Sierra told me there will be no more. Luckily I bought 900 from Jamison's before they folded. If you want bullets custom makers are really your only choices and you can expect $2+ per bullet for these. 30-40 loaded rounds will eat 1 can of Retumbo.
IMO the point of these rifles is to hit things Waaayyyyyyyyyy out there, so accuracy and precision are the most important features. Starting out skimping on componets for the build will only compromise the accuracy potential of the finished rifle which is just cheating yourself, and you could possibly end up with a rifle that is a letdown, and likely as hard to sell and get rid of as yellow snow in Montana.
My advise is if you really want one of these big rifles and the cost to feed and maintain the big girl is not an issue.....just save a little longer and buy the best of everything and have someone that is familiar with this big cartridge build it for you. I know it's hard to wait longer but I think you will be glad you did in the long run, when you end up with an awesomely accurate rifle made with the best of everything. Best luck!
Stiller or Defiance is probably the best compromise between price and functionality.
Do you have actual knowledge of Defiance building a repeater action that will support 375 or 408 CT? Their site (price list page) notes the largest as having a .750 bolt, typically what folks are using for 338 LM, max. I know of no other "retail-available" action that is 408 CT capable and a repeater. Snowy Mountain has no bottom metal and in no big rush to close that loop. Xtreme lists one but I find no consistent good feedback on them or their cation - I hope to do some hands on at SHOT. The only other repeater solution seems to go 50 BMG size and see if you can get the manufacturer to build one with a CT bolt face - with "standard" multi-unit builds seems most actions are built all one size per setup and a one-off bolt seems unlikely.
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ELR...anything shorter is point blank!