Is it possible to, when switching instruments, for the staff order to change to reflect this? For example, if flute 3 doubles on piccolo, I would want the flute sections to be below flutes 1 & 2, but the piccolo sections to be above flutes 1 & 2.
IIRC Not possible (at least not at this time).
No, it’s not possible. Staves for instrument changes are always adjacent at present.