I'm not sure I'd want the system 'weighted' but in general I support a lottery over the current system.

When a plot is vacated, you pay into the lottery to relocate or to purchase the plot. Say a 48 or 72 hour period so people have time to stop by and pay in.

If you win, the transaction goes through. If you don't win, you're refunded your gil via mail. Or some sort of retainer esque npc you can deplosit gill into/withdraw from for the sake of this lottery.

This way people don't use click bots. People don't have to stay at the plaque not knowing when the timer will end. You stop by, put your name into the hat, and you can move on to other things.

I don't know how hard it would be to implement but I really see no downsides to it compared to the current system.