Measuring AC phase Question

I wouldn't rewire the outlet. If you're really intent on reversing the AC polarity, buy a power cord which you can access the plug wiring. Reverse the wires in the plug, instead. This way you won't need a cheater plug nor to shave down the oversized prong.

Keep in mind, though: correct AC polarity sends power first to the switch and then through the load. Reversed polarity sends power through the load first, so there is potential avilable with the switch off (still energized). Possibility of equipment damage and injury is more likely.

Remove the neutral wire from the outlet and measure the voltage from the nuetral to ground. If this is 10 volts, then you have either a high resistance in the neutral, poor utility neutral connection, or the neutral is not grounded properly at the panel. Other possibilites are high neutral currents (harmonics) from computers, fluorescent lighting, and motors, and neutral and ground wiring either interchanged or in contact with each other somewhere in the house wiring.

Some manufacturers bypass the UL rating with the 2-prong outlets by selling direct (no dealers). The reason is to minimize ground loops. The safety factor is using power supply transformers with 2,000 MOhm primary resistance, which effectively limits the current from either of the mains to chassis (ground, in this case). The neutral of the 2-prong cord is isolated from the chassis, but it still can pick up the stray current from the wiring system.

A ten volt drop across the chassis is high. I would contact an electrician to check the service wiring and grounding, including testing ground to earth resistance (should be less than 25 ohms) and to install a dedicated circuit for your gear.