it shouldn't be impossible for anyone to acquire a large in Final Fantasy 14. If they have the gil for it. So here is what I propose:

I don't know what the EXACT character limit is for each server, so lets say the limit is 2000.

If there is 2000 characters maximum in a server, then there should be 2000 housing plots in a ward. Each character is only allowed ONE housing plot (not 2: 1 for personal, and 1 for FC), where they then have to honestly sit and decide if they want a personal, or an FC house. If they choose FC, then they still have apartments, and FC rooms for their personal space.

After that, EACH plot should be able to fit a large size house, but have the ability to start off with a small. Give the players the ability to work their way up to a large if they so choose. Some people have mentioned this may cause issues with server lag cause of trying to render in furnishings and such, but to counteract that, just have the housing districts have less plots, but more wards.

In the end, both the previous method of having to sit and click on the placard, and not being able to do anything else hoping for the invisible timer to end, and the lottery system, are both very poor methods for trying to purchase a house.

Only other method I can think of is individual instances for your House/FC building. However, I know Yoshi-P likes the idea of having neighborhoods, and I respect his feelings on his game. But something has to be done, so everyone has the ability to own a large.