I left a comment on @jermn 's reply but wanted to share some pictures to accompany the text. Jeremy's approach worked for me; I found his suggestion to open up the side especially helpful.
I, too, broke the tab while trying to fix the issue. So, I proceeded to open up the side of the printer. I found a metal clip that forces the white piece to disengage when you pull out the paper tray. If you insert and remove the tray while the side is open, you can see this in action. This seems extraneous ... why not keep the white piece, and thus the gear, always engaged? Since I broke the white tab I figured the white tab will get out of position again in the future. So, I disengaged the metal clip, snapped the white piece into position so the gears are engaged, and replaced the cover.
Side view, after disengaging metal clip:
[image|1344666]
View from inside the paper tray slot:
[image|1344668]
The printer seems to be working like a charm, and I've got clear steps to follow in case it gets out of position again.
It works!
[image|1344667]