The remage comes in 1-1/16x16 tpi so if your action doesnt have those threads then you cant use the remage systems as they come on the shelf. Often times truing an action involves cutting on the threads which would change it from the factory spec. If they didnt touch them on your action and they only squared up the face or something then you might still be able to use a remage. I cant tell you that though.
I mean Im sure you could have something done up custom but that would probably exceed the cost of a shouldered barrel.
Northland shooter supply has the criterion set up, mcgowen, , xcaliber and the spr bugnut are the other players I think. I went northland with a criterion.
As to whether those actions you listed have the regular remington thread specs I cant say, I dont know that info and its not on their site at first glance. If they dont then they may have the savage specs which would be nice, I think bighorn and mausingfield are savage small shank. All remage is is taking the barrel and rather than cutting the shoulder to time it correctly you use a jam nut to hold it in the correct space. An arbitrary shoulder. Remington-savage=remage.