Product review (5 stars): I put the old unit in and it dispenses ice just like the new one
I purchased a complete new unit then came up with the idea below.

I got a hose clamp 1 3/4 x2 3/4 from the hardware store. You undo the clamp completely and slip it over the broken part slip it as far back as you can,  and tighten it down. Make sure the split in the piece is closed. I put the old unit in and it dispenses ice just like the new one.

As I just did this I have no idea how long it will last, but if it does not I have a new unit to put in.