That is entirely too much voltage drop on the solenoid-to-starter side. So it sounds like you need to isolate whether the problem is the cable or the solenoid. Run your voltage drop test across the solenoid. If the voltage drop is still 0.09-0.13V, replace the cable running from solenoid to battery. If the voltage drop is 1.0 - 1.3V, you know the solenoid has seen better days.