The rifle needs to be made, or the free brass won’t be of any use. If a 1.35” action such as a 700 or 70 was ideally suitable for a 30-06 on which somewhat smaller and larger cases were anticipated, then at twice the weight+, a 1.45” action is the proportional scale up for the .338 LM that fires twice the powder charge and bullet weight.
Remington has chambered .338 LM Police on the 700 as a factory offering. But that “first ring of steel” sure was thinned out to make room for the big case head. That bolt was clearly not intended for cartridge heads larger than standard magnums.
Granted, a wider bolt body is not common. That part of the bolt is more of an aesthetic issue than anything else while the gun functions normally, at least, but it would be a constant reminder I’m pushing the envelope here. It’s also true that most actions use the same two small action screws, (Savage up to 3) however all 1.45”’s I have seen have about 1-1/2 or 2 more threads of engagement.
There are some things that a larger action brings to the table that are of benefit in every shot, as opposed to a failure situation. The larger action implies a thicker tenon with more threads and a thicker shank those first few inches, to counter the fact that a .338 LM removed a lot more steel from the tube than a .308. No one objects to thick walls.
I don’t know of any 1.45” actions except maybe the P 1000 bench rest by Stiller that don’t have a massive recoil lug, usually integral. Bat does tend to use slotted, screwed in massive recoil lugs, though. Also, you usually get an integral picatinny rail with the large body actions.
An integral rail is three benefits in one. It never comes loose, it adds to the rigidity of the rifle instead of just being neutral, and in the case a .338, the rifle will probably be paired with a large heavy scope. Even if you red loc tited the base down such that the screws never came loose, would you ever really feel as comfortable with tiny screws securing three pounds of base rings and scope on a hard kicking gun? I never have even when the good bases I use have their own recoil lug.
But for the price of an action, there is a Savage single shot rifle in a laminated stock that shoots custom rifle sized groups. No TRG 42 for multiple dollars - a great gun by any standard, is safe when this Savage comes around.