Yes, that procedure was already working for me. What I saw in the training video was clicking a month or sub-category name directly on the header (January or Bookcases) and dragging it to it's new position without needing to open the menus as you've shown. Is there also a shortcut like this? I can't find the video where I saw it at the moment.
I think I found an example where re-ordering of bars for a date was possible. But I don't yet understand why it works only in some cases. Please see the video below.
- Years only: cannot re-arrange bars
- Years + Quarters: can re-arrange bars
- Quarters only: cannot re-arrange bars