As everyone knows, the Epson has no power clean mode. Therefore, if you have a serious clog, you have to use the paper towel under the head, or in really bad cases, use the initial fill routine from the WIC utility. However, could one use a syringe on the waste ink line and slowly pull ink through, imitating the action of the vacuum pump? I assume if that has any chance of working, you'd still have to run a clean cycle that would run the wiper under the head.
It is just a thought. If it's ill advised to do so, perhaps this is the place to warn against doing this.