How long ago did the Epson tech service this printer, and exactly what did he do? Were the LC and LLK positions working well after he left?
I see you originally bought refillable carts and ConeColor ink for a 7900/9900 printer in Feb 2011, then recently bought two sets of new model carts with PiezoFlush.
Is this the same printer you were using in 2011?
How often is this printer used, vs how long does it sit unused?
When did the LC and LLK channels start not fully printing?
What happened shortly before they stopped printing- had the printer sat unused for a while, had you been printing a lot, had carts been refilled, etc...?
Dampers are not cleaned, but should be replaced every 1-3 years (the dampers come together as one unit, called the "ink selector unit" with this model).
If the dampers and/or print head channels were clogged in these two positions, then nothing will flow thru and PiezoFlush can't reach the source of the clog to clean. With a total blockage restricting all flow thru those two channels, you will need to start by replacing the ink selector unit, and I'd try flushing the print head while the dampers are disconnected and head is exposed- but these heads don't respond well to flushing like previous model heads, so that may help, but there's no guarantee...