Instead of complicated solutions, just remove limits on switching GC
For a start, I think the focus should be on trying to swiftly end the frustration of GC PvP population imbalances inflating queue times, restricting freedom to play with others, and confusing new NA/EU PvPers who don’t understand why everything seems so broken.
Given limited developer resources, I think the simplest (crudest) solutions have the best chance of being implemented, especially in the short term.
So how simple can we get, while still improving the situation?
Completely remove cooldown on switching GCs (ie, edit a variable)
Completely remove the fee for switching GCs (ie, edit a variable)
One shared PvP Ability Rank (AP pool) across all GCs (possibly more complicated than editing a variable, but hopefully not much)
And to support those changes, some additional bonus improvements that might be crossing the line into ‘too complicated’:
Show how many of each GC are in the queue, or at least clearly indicate which GC is currently ready to play and which GC is currently waiting for more players
Grand Company in Need bonus for whichever GC is suffering minority status at the moment
If deemed necessary, make this a feature that each player unlocks (because FFXIV loves giving players stuff to grind and unlock), possibly with a fluff quest attached (like the Beast Tribe finale) acknowledging you as ☆Special☆ for whatever you did to unlock it (and thus allowed to fight for whichever GC you choose to at-will).
I think this band-aid would be sad in some ways (currently, there’s a definite personality and community within each GC on each Datacenter), but I also think the benefits of removing a lot of the factors that create deadlocked and stagnant queues would outweigh the sentimental losses.
However, the most useful thing for the developers is our discussions, criticisms, arguments, etc, so please speak candidly about whether you feel this idea would improve the overall situation and your personal frustrations with the current PvP system.