I've tried all the ideas, and:
Beepster - Dragging the tabs out and then back in the desired order doesn't work as it memorises the order they were in originally and snaps them back there. Seems as if you have to close and re-open.
Steve - the quote is from page 976 of the full manual. It says just a single sentence under the heading To Rearrange Tabs, "Drag the currently-selected tab to the left or right in the tabs area."
AJ - Tried it both docked and undocked but makes no difference.
BJ - Tried the modifiers again both docked and undocked but again, makes no difference.
Bluzdog - Your idea would work, but you'd still have to physically close each tab and reopen their respective views or plugs to reorder them for each screenset.
So in conclusion, it seems it can't be done. Feature request for the first X2 update methinks. Unless the first build can do it, that is. Within my cloudy, hazy memory, I'm sure it was possible in 8.5?