first - the back gear is no big deal. I rebuilt mine in about 2 hours, including taking it off and putting it back on again.
(okay, the jig I built to handle the head took a couple of hours to build also... truth be told)
Mine works like a charm now.... but you simply don't need it. I took out my back gear recently (long story) but my VFD handles ultra low speeds better than a back gear. Sorry you have a phase converter - my bad! You can rebuild the back gear fairly easily, and all it really needs is a clean and lube. It relies on gravity to engage, so when it's dirty, it won't engage easily until it is clean and greased.
Now a lower rebuild - I haven't tried it, but I need to!
[edit] From your pictures, it looks dirty and dry. that's likely to indicate a bunch of dirty dry grease is preventing the thing from engaging.