Error message carriage jam and/or paper jam

I've diagnosed the problem for my phantom carriage jam, the issue is in a small gear assembly to the right and below the ink cartridge maintenance tray. There are three plastic gears in this assembly that drives the paper feed and the ink cartridge maintenance tray. The black plastic driven gear in the middle that the metal drive shaft attaches to has a split in it allowing the shaft to split, this consequently does not move the paper feed and this comes us as a carriage jam.

This foreign page details the failure: http://www.istorya.net/forums/computers-and-accessories-59/544066-gear-set-hp-photosmart-c5500-series-hp-c5580.html

Here's a foreign video about it:
https://www.youtube.com/watch?v=4PCUmouo0-E

This is the small gear:
https://www.google.com/search?q=hp+photosmart+c5580+carriage+jam+gear&espv=2&biw=1920&bih=955&source=lnms&tbm=isch&sa=X&ved=0CAgQ_AUoA2oVChMIw-_uhcmhxwIVDpaICh0ccwiC#imgrc=u1by5ja5gYX_jM%3A

The gearbox just pulls off the shaft and is disassembled be removing the small metal clip and unhooking the catches on the side. I've fixed my split gear by turning a groove into the small gear on a lathe and gluing in an aluminum ring to stop the crack opening up.