Those guns are built on a large Martini rifle action that is hell for strong. Some are takedown and you could (with some $$$) add a rifled barrel to it. PERSONALLY I wouldn't rebarrel a nice example of the solid frame version; they're not making any more of them, and you could probably find a large Martini action to rebarrel cheaper and easier. Model 12 Winchestr semi-finished stocks are very easy to convert to large Martini stocks. Just avoid any large Martinis from Afghanistan; lots of modern (and older) fakes coming out of there with "railroad track" iron!
The only thread specs I could find for these is in Frank de Haas' "Single Shot Rifles and Actions" where he shows a diagram of the large Martini action (rifle) and says the barrel thread is "16 tpi v-thread." In the back of the book, he shows the later .303-chambered Enfield Martini as "14 tpi v-thread." My GUESS is that the shotguns are of the later standard, but that's just a guess. That book briefly discusses converting a .577 Large Action to 12 guage.
There's a Martini Forum on
www.gunboards.com/forums that will answer all your Martini questions, I think.