It literally doesn't matter if you bought your house without knowing Shirogane was coming. You bought your house. By the very rules of fairness that you implement, you have the money or you don't. That's what makes it fair. You got use out of your house. You will continue to get use out of your house. It wasn't money wasted.

Now people who have the money will buy houses in Shirogane much how you did in the Lavender Beds.