Talk you out of it? OK. My old 16 ga. would drop a shell on the ground when working the action for the 2nd shot. It would load the 3th shell. When the shell comes flying out of the magazine, it may be set off as the primer area hits the receiver. Had a 12 ga that would not shoot reloads unless the brass was fully sized. A Mec 600jr was not good enough.
most likely that was caused by a couple dollar spring getting soft or the channel that the left hand shell stop rides in being gunked up. That is a common issue with Ithacas that get a bit old or out of adjustment. The fix is to clean the channel and put in a new spring.
on the older guns there is a screw that holds that stop in, on the later guns it was changed to a pin. if the screw is tightened all the way in, that can cause a bind also.
At worse, sometimes the nose of the shell stop needs bent out a bit.
Ithacas do need to be cleaned once in a while. A simple way is to pull the buttstock off, hold the gun with the barrel pointing up and spray it with brake cleaner, work the action through various stages and spray, turn it over and spray it out from the back.
Then give it a very good lubing after that. A good cleaning cures most Ithaca 37 ills.