Richard - I know what you want me to do, but did you know that you cannot set the orientation to Portrait (or anything else) while the "Lock rotation of this display" is set to OFF?
So here is what I did:
1. Kept the Lock rotation button to On.
2. Set the Orientation to Portrait
3. Clicked on Apply (if you skip this step then turn the Lock rotation of this display to OFF, it resets the orientation to Landscape). As soon as I clicked Apply, the monitor switched to Portrait orientation.
4. NOW I set the Lock rotation button to Off, and the monitor remained in Portrait orientation. (Clicking apply at this point in time has no effect as it is inactive until other changes are made in the Settings/Display window) Then I closed the Settings/Display window and the monitor remained in Portrait orientation.
Then I tested this configuration by clicking Start Lock and it displayed the Lock screen in Portrait orientation. I then entered a Ctrl/Alt/Delete and was taken to the Login screen, again in Portrait orientation. I logged in and was shown my desktop, again in Portrait orientation.
However, when I signed out, the monitor switched back to landscape orientation. I have tried this about a dozen times and it does not work. Got anything else?