Two Factions would like to change positions in the Galaxy.
Other than dissolving both Factions and recreating them in the proper HQs, is there a way for them to switch HQs?
Get both factions up to where they can have a 2nd HQ and build in the right area. Then when membership goes back to normal, unprotect the extra HQ in the wrong area and trade it with the other faction, then both have 2 HQs
Just remember the limitations imposed on a faction without an HQ, if that's the only one you have. Read up on the rules thoroughly so you don't make mistakes.