So you will still end up with rich people watering their lawns, but people with less income will have to suffer. I think this is better handled through heavy taxation and outright bans rather than trying to get an already finicky thing like a market to solve it.
Tweaking the market and exemptions might be difficult and finicky. But managing taxation and outright bans is even more finicky.
I am not, btw, arguing for an electricity like system of daily auctions. Just for a 2-tier pricing system that covers the basic requirements with a low rate, and sets a roughly 'market clearing price' for the remainder.
For this I would also price untreated water quite a bit higher. The price isn't just set for the cost of extraction. It is mainly set for the opportunity costs of all others who cannot use that water. So untreated water should cost roughly the same.