I hadn't looked at this before, myself. I guess my sketching in LO is just that. Not used for precise work. I kept experimenting to see if there was some trick. As Dave says in the last comment, as way to change the handle of the widget--if indeed we have to continue to use the widget in the future... I imagined using a modifier key that would "free" the rotation arm to be realigned.
Other notes. I don't highlighting mentioned in this thread. It is so light on my computer I often can't tell if it's really there.
I guess you have to measure the angle then do the move by entering it. This is not that easy, given the odd ways LayOut does things, but I guess you can learn to avoid the pitfalls.