I've not tried to move the default bars, but have an addon called "Move Anything".
It has options to check, which while checked allow things to be moved.
Or another option to hide things.
There is a check option to move the default bars.

So the gryphons on the default bars are hidden for me, as are the Druid stance bars.
I still have them keybound and the keybinds work fine, but they're hidden and out of sight.