Sounds like my idea of what to expect was wrong.
Let me back up for a minute and explain why I was even checking the resistance in the first place.
This is a used Autoformer purchased from CraigsList. I plugged it in at a campground here in FL where we were camping for a week and it resolved the low voltage issues that we were having during peek AC usage (2-3pm). However, at some point my daughter got a little bit of a shock on the metal door handle and I thought it might be the Autoformer so I unplugged it and it went away. That is when I noticed the corrosion/melting on the plug.
I decided to check if on of the plugs was shorting to ground, which they weren't, but then I noticed that there was measurable resistance between hot and neutral and wasn't sure if that was expected.
I have thought about wiring the unit directly, but I want to be sure that it does not have any other issues before doing that. For now I have changed the plug, and hopefully that fixes it.