Edited to add: I just opened it up and the heating element is still hot, but the error light (7 blinks) is still going. I don't think that this was one of the expected results.
Well we now know that the heating element is working.
Trip your breaker or unplug the unit. This may be required to clear an error.
Though they do say running the diagnostics will also clear the error.
May also be other methods that I do not know.

Next would be to check the temperature sensor (thermistor).

Control board?
This is starting to look like the most likely culprit.

I reset the error (using the self diagnostics) and will reconnect the door switch.
I would leave this shorted till you run further test

How do I test the thermostater?
Thermistor
Check it for resistance. Item 25 in Pump and Motor section.
Tech sheet gives the acceptable values. Sorry my computer will not load the tech sheet right now.
Note water may drain out if you remove it from the pump.

Thermostat
Also, I would like to confirm I hooked the thermistator back up correctly. I attached the two wires to the thermostater terminals. The third terminal (attached to the bracket) is left open.
Yes this sounds OK

if I understand what I am looking at, I am supposed to test the temperature heating circuit.
No you have already checked the heater circuit and it is OK.
This is the temperature measurement circuit.

the resistance should be 48-52K ohms at 77 degrees and 12-13K at 140 degrees.
This is the thermistor which measures the water temperature. If during a water heating cycle it does not see a change in temperature/resistance, it will give you an error

Do I test both high and low? If so how do I do that. Do I pour water into the machine at a known temperature?
Test the low (room temp) first. Remove one wire from it or the plug (if it has one) and measure it. It should be around the room temp resistance area of 48 to 52 Kilohms. If yes you could then measure with some hot water added to see if the resistances drops.
If it does measure 0.5 ohms remove it from the machine.
If it still measures 0.5 ohms when removed, it is faulty and needs to be replaced.

I think we checked this before, and we received .5 ohms (basically zero).
I do not remember testing it.

Am I now supposed to test it with the machine plugged in?
No, it is a standard resistance measurement so power should be off.

If the above component is OK then all that is left is the circuit board and it will have to be replaced.

The upper range on your meter is a little low.
Stick it into a cup or hot water and see if the resistance drops to where your meter can read it.
If it does not drop then I would order a new one

You have checked the following and found them OK
Door switches/latch
Complete heater circuit
Temperature sensing

So by the process of elimination all that is left (that I can think of) is the control board.
I would order the board.