Measuring AC phase Question

I understand I am to reverse the plug in the AC outlet and measure from a known ground, in my case, a galvanized water pipe, and the positive probe is connected to the equipment chassis. I use a cheater plug on the power cord to allow reversing of the orientation. No other cords are connected to the equipment being tested.
You are supposed to choose the position of the cord that yields the lowest ac voltage on the chassis when the unit is on.
The problem I have is that the lowest voltage with the switch on also has by far higher voltage on the chassis when the power is switched off.
determine the best phase connection, then rewire the outlet, if necessary, to reverse phase internally. This eliminates the ground cheater adapter & the chassis will always be at ground potential, theoretically reducing stray measured leakage voltage to zero. Label the outlet prominently so that you don't accidentally forget that the hot & neutral slots are inverted. This could be a safety or liability issue in the future. Disclaimer: I am not (professionally or otherwise) advising that you invert these electrical connections. I am only "answering your question". I'm sure that you understand what I'm implying.
Purchase a cheap phase polarity meter and check it. These can be bought at Sears, Home depot, etc. They also have a ground orientation mode. Remember, AC has 1 hot leg(usually the black wire), 1 neutral(white) and a ground. The neutral is tied to the ground buss along with the ground but they are not the same thing. Reversing the polarity can create problems sometimes. The switch on the unit generally opens the black wire. If you reverse it, it now opens the white. It something unexpected happens, the chasis of your unit could remain hot(worse case scenario.)
Two items that may be important:
First, are you measuring the equipment in isolation? That is: nothing else is connected to the component being tested?
The equipment should be in isolation, even all the interconnectors off!, or voltage from other equipment will skew your results.
Second, are all your components plugged into the same wall outlet (both plugs or four way unit of one service recepticale?) if not, then you also may have a problem with the different outlets being wired differently (you can check this by using an ordinary light bulb in a socket and two probes: insert the probe into one channel of the wall's outlet and the other to ground, then test the other wall outlet A/C opening and ground,... one should light the bulb... all you outlets should have the same side light the bulb when the other leg is to ground.
Secondly, check if the 'hot' side of multiple outlets have a 220 voltage differential. If the two different outlets are using different "legs" of the standard 220 three wire house voltage, you could get some odd stray volatage readings (I am not explaining this properly as if I were an electrician, but I hope it makes sense)
And I would NOT change the wiring to reflect you units preference, I would open the unit up and swap the wires at the units A/C connection to the A/C wire, or to the chassis IEC connector.
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.
First, are you measuring the equipment in isolation? That is: nothing else is connected to the component being tested
that question is already answered in the posted text.

If you decide to go inside the equipment instead, then annotate the mod such that it can be reversed later before any future sale - otherwise it's now modded / nonstandard equipment with diminshed resale value & may not pass the U.L. If it blows up later then this could come back to haunt you.
thanks for your suggestions so far. All tests were done with no cabling connected. Each unit came with a two prong plug with no ground. I did replace the attached cords with a IEC receptacle. My concern is the high voltage on the chassis when the unit is switched off. On one unit, it measures 10 volts.
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.