I was unable to try Epson Adjustment Program to correct skew problem myself as the printer was already at service center, but they told me that no software adjustment was enough to fix the problem. So they sent me another one.
The new printer has almost none existant skew but entire printing area is still shifted 1mm right. It's easy fix using an offset setting in the driver properties, but I'm curious if I will be able to make this permanent using this software when it arrives.