So I did a bit of research on the "slam firing"...

There's three parts involved, the hammer, the slide stop and the bolt carrier. It actually works a lot like an actual M16 with a full auto sear.

You press the trigger, drop the hammer and it fires now with the trigger held back the bolt carrier comes back and depresses the hammer, as the bolt carrier returns forward the hammer attempts to follow it home except it's caught by a nub on the slide stop (or action release), the carrier continues back into battery and a small leg at the end of the carrier trips the slide stop to release the hammer to drop again for firing once the bolt carrier/bolt is now 100% into battery.

The slam fire "feature" is actually apparently a safety device that prevents an out of battery detonation (real slam fires).

All I could fine online was pictures/diagrams of the old trigger group and not the new one so I can't compare 1:1 however it seems like the newer shotguns do retain the old bolt carrier and maybe even the old slide stop, so the only thing that might need to be changed is the hammer. Apparently according to some knowledgeable Ithaca smiths on shotgunworld forums new Ithaca shotguns can be converted to the old design, a member on there that claims to be a dedicated Ithaca smith says all that is required for parts is the old slide stop and hammer. I'm assuming one would have to remove or disable the trigger disconnect found on newer guns as well. I don't know what this even looks like or how it works, it might be as simple as removing the part or filling off where it interfaces with the trigger or it might be a huge pain where the whole new trigger group assembly is designed to work with the disconnect and not work without it being installed. Lastly, the new Ithaca shotguns are 3" shell capable, the old parts capable of slam fire seem to be listed for 2-3/4" with separate new parts for the 3" guns, now does that mean it won't work or you'll lose the 3" capability if you use them, I don't know.