Part 1 - Instance and Ghost housing
One solution would be this:
(Instance house/or maybe even plot housing)
Have an NPC that sells ghost plots. Meaning paying for a plot that doesn't exist in the game. So long you have the money you can just pay it.
Pros: Zero randomnesses, Zero obstructions and 100% availability so long you have the GIL.
[If instance]
Then once it is paid, you will immediately receive the plot
[If normal plot]
Then once it is paid, you wait for the next "Ghost housing implementation patch day" where Square Enix will launch those houses for people used the NPC to buy the house. That way there will be no oversupply and won't stress the server. You will get it eventually maybe wait for a month or two instead of never getting it. This will also give you (developers) time to put in plots/wards that will balance out demand/supply. Everyone will get a house, so long they can pay for it. That should be the only ceiling of getting the house.
Also, 1 house for personal and 1 for FC. This is key.