Epsons are tough to unclog because the printhead isn't part of the ink cartridge(s). HPs give you a new printhead with each cartridge change.
The only way I was able to really, really unclog my Epson C88+ heads was to get a small medical syringe connected to a small piece of tubing that fits over the little stub that pierces the bottom of the ink cartridge. Under the print heads, I put paper toweling. In the syringe is Windex. The ammonia in the Windex dissolves the dried, clogged ink as it's gently forced through the tube.