How to unclog yellow ink on brother mfc printer?

At home, I have a Brother MFC 665CW purchased a few years ago. I know it is older but I've figured out how to make it last this long. I have been refilling the ink cartridges with Jet Tec refill kits (http://www.jettecrefill.com) and that has helped me keep the printing costs down.

My current issue is that the Yellow ink has become clogged. At first I thought, I'll take it apart and clean the printheads. You think that is easy? Not exactly
take out tray
take out ink
unscrew and remove front panel
disconnect wires to front panel
disconnect wires to auto document feeder
disconnect wires top scanning unit
unscrew top cover
discover that printheads are assembled in bizarre unservicable location
put it all back together

So that was 4 hours wasted

Anyone have ideas on how to unclog this yellow ink?

Is there a cleaner or substance I can...