It's stricly the same that i show in my post above! ;) (i try of course with your 2 objects)

As I take the normal base face with the Helpers Line ... faces of the 2 objects will be // so i can make the trick of the first video! ;)

I made as i said 2 Line-line...

Object is not aligned when the mouse is not on the face ! ;)


If i want the same result than your i stop the rotation when Helper Lines said 90° (or I type 90°)


I am agree it's 2 functions against one but I have the "scaling" more inside if wanted! ;)
And I am more fluent with the Line-line that the rotation ;)
And it's my favorite function! ;)