The Jameco ReliaPro UL Listed DC converter (rated at 6VDC, 800 mA) delivered 8.0 V.
The DC converter rated at 12V delivered 8.5 V under load and the one rated at 9V also delivered 8.5 V under load.
Assuming your 750mA load, nothing here matches up with what is expected. Except that I would expect a 800mA rated supply to be in regulation, not wildly out of it.
3) The 7805 voltage regulator is described here: addicore.com/Addicore-L7805CV-5V-Voltage-Regulators-5-pieces-p/114.htm
A TO-220 package can handle SIGNIFICANTLY more current than the tiny sot-23 package used on the Arduino board....
Oh, dear, In the process of measuring the current and voltage, I bypassed the voltage regulator in order to reproduce the erratic behavior that I described previously. I, um, fried my Arduino Micro.
Changing connections (including measurements) should not be done while the board is powered. If you're moving probes around while powered, your attenshion (your eyes) should 110% be focused on where the leads are going.
Yes, I know, the Arduino Micro max current is 50 mA.
I'm not sure where you got that from. The max current that the 3.3V rail is rated for is (erroneously) 50mA. (It's actually 150mA).
The 5V rail is rated for whatever you can draw until it shuts down, and that depends on Vin.
However, let's keep in mind that this current is not going through the Arduino (see schematic).
I'm confused. Has this been your setup the entire time, or just after adding your own regulator?