The 3-10-39 Ithaca bore and choke drawing on the linked thread is gone due to the Photobucket hostage taking a few years ago, so here it is from Imgur --



and for comparison the 7-8-34 Choke For Skeet Gun drawing --



My Ithaca made doubles with S and S choke markings are --

Fully optioned 12-gauge No. 4E .009" right and .016" left.

Lefever A-Grade 20-gauge .008" right and .014" left.

Hard to say what may have been done to chokes in these old doubles since they were built 80 to 130 years ago, but I'm pretty sure choke wasn't added.