For my Win10 desktop, I used the REGEDIT solution above. After a clean install of Win10, I had a test monitor plugged into plug 2 of my graphics card, since is my HDMI native connection.
The monitor I wanted as #1 AFTER my original testing, needed a Displayport to HDMI converter. When I plugged that one in, it would also be seen as Display 2 in Win10.
Rather than delete the following entries, I just renamed them:
(In my case I renamed to ...ConfigurationOriginal, and ...ConnectivityOriginal just to make it easy to revert if needed.)
I turned off the machine, unplugged everything but what I wanted as Monitor 1, restarted and it booted to Monitor 1.
While in Windows, I had the Display page opened, plugged in Monitor 2, then Monitor 3 and they came up and numbered exactly in the order I wanted.
Now my monitors match the connections in the back of my graphics card, going from one to three, from left to right.
Easy to remember.
I also looked at the new keys via Regedit, and Windows recreated "Configuration" and "Connectivity" and now has the three monitors I'm using.
Worked the first time, took less time than writing this THANK YOU message to triadiktyo for posting a working solution.
Monitors identified correctly, in the right order, everything works as expected.