Re: cheapest .338 lm action ?
If you are trying to get into the 338 LM game as inexpensively as possible, you might do better by purchasing a Savage FCP in 338 LP for around $1,200 or so. I hear they are shooters and generally hold to .75 MOA or less.
You get the action, 20 MOA rail, a decent stock and a decent barrel. If you like the 338 LM game (it can be expensive), then you can begin to upgrade from there. I am currently pulling parts together for a 338 LM AI build. More than once I have cried about the money involved and have been tempted to sell off my parts and buy an FCP.
I have a Stiller TAC-338 for this build and I believe you are correct in that it is the least expensive action you can get for a custom build. You may be able to find a gunsmith willing to make a single shot 338 LM for you based on a Rem 700 mag action, but fewer and fewer are willing to do so.