How I did this in 5 minutes: removed the paper, taped a small mirror on the paper tray bottom, turned the printer upside down, and dropped superglue drops on the spline, using the mirror to position. I added a few drops on the side of the repositioned gear but that might not be nessessary.

NOTE: make sure the due-ink-reservoir (underneath the parked cartridges location) is emptied with a cloth before turning the printer!