A less radical option would be to keep the system of water rights we have today and simply allow the water to be bought and sold. Currently if you sell it, someone can take you to court & say "well you didn't use it, so you should lose your water rights" (because California follows the doctrine of first use). Would run the risk of creating wealthy water czars overnight, but less radical.
I have no idea how first use could work for water, would be happy to read more if you link me to something about it. A quick googling returned nothing.
The last one requires a lot more specifics to talk about meaningfully, but I'll bet that most of the free marketers wouldn't consider it a free market.
So one way of looking at the whole problem is to ask why transaction costs are too high to make this feasible. And the obvious answer is politics.
California is both an example of how markets can't handle water, and has also never had markets in water.
To put it another way: if the users being asked to conserve water could just pay farmers to use their water, both would come out ahead. The farmers would get more value than from using it for farming, and the other consumers would get more water for a lower price than from alternatives.
In any case, it's bizarre you cringe at the word "markets". Societies that try to avoid markets are horror shows. Markets are an utterly essential social technology for the modern world.
At all.
The water issues in California could be addressed by trading (say) half the water currently going to agriculture. Everyone would be better off, including those poor you pretend to care about.
So your idea is that the government will decide and enforce that roughly half the water is not allowed for agriculture?