I had my model 37 threaded for choke tubes years ago by Briley. One problem that they brought up was that the barrel was fairly thin (one of the reasons that Ithaca called the gun Featherlight). The were still able to tap it and sent me a super full choke tube fitted to the tap. Now, the barrel on this particular gun was a cylinder bore with rifle sights and it still worked. If you are starting out with a full choke, there would be more metal there and would make the machining that much easier.
Buying another barrel to tap is certainly a good idea for preserving the value of these great shotguns. Be aware that another barrel to fit it might cost you more than the original gun.
Good luck.
SE