I was trying many things and the tab separation seems fixed...
What I can suggest is disabling the tabs (not visible) and replace them with overlapped toggle buttons, each button should activate a tab and on toggle, you will need to uncheck current button and reorder all the buttons.
Pressed and released textures will do the rest of the effect.
ps: Overlapping tabs is a cool and not uncommon visual effect, you can make a feature request for that if you wish.