You’re welcome, fingers crossed it is a simple fix. It does look like it shouldn’t have room to move enough to come out of engagement, but if the damage happened to the original owner, it might have been run that way for a while and worn the housing enough to let it move far enough to come out of engagement. I’m hoping that is not the case, but I think you need to take it apart and do a thorough inspection. If that is what happened, it looks like you can take that part off the carriage and sleeve it back to specs, and hopefully not have to make the worm gear.
I bought metric lifting eyes from McMaster-Carr, they should have anything you need.