So the good news, bad news.
These are fantastic, but they do not work as a retro-fit to and existing 1x1 flush mount can light.

If, when you take down the exiting fixture you have a flush mounted 4x4 gang box - you are good to go.
If you have a 1'x1' nominal opening in the sheet rock and a fixture mounted to the studs..you are going to have to put in an LED lamp and move on.
Or you can wreck out the fixture, frame the opening and set a 4x4 box and go from there.

I was away - but I have worked with this Electrician for years and the plan we had cooked up on the phone/email did not survive first contact with my slopping ceilings. There was no way to keep it square with the opening.

I have not sent them back, thinking about re-doing the lighting in my home office....

But if I was doing this in a new structure I would not hesitate.
I ordered them from Home Depot, they did not stock them at a store close by.
Very well made, commercial grade fixture - they were about $80 each.

Let me know if you have any other questions. Sorry this did not work in my location but it was not the fixture - it was the pre-existing conditions.