Once the hammers and their main springs and followers are out, the firing pins are held in position by long,tiny set screws.
Those set screws are heavily staked into place in factory assembly. They rarely come out easily. Other Ithaca's have the same set up. Often it takes drilling them out, re-tapping and replacement of the set screw(s).
Once in a while you get lucky and one or both turns free.

Reassembly is easy with a jig to hold the springs and followers down. Near impossible with out one.

Some people have resorted to tapping the frame for set screws to jam the springs and followers in the compressed position (same idea).
But altering the frame never seems like the best course to take even if the 'work' is covered up with the trigger plate when assembled.