I'm in the same boat. I have nasty clay soil.

Somehow you are going to need to create an evaporation pit of some kind. If you are familiar with septic system drainage fields ... they don't drain fluids down - they evaporate them up. You are in a position that you have to do the very same thing.

My thought would be that when you bury the business end of the hydrant rather than just fill it in with clay, you line the pit with landscaping cloth, and then fill the pit with some kind of "sharp" gravel with limited "fines".

I'd talk with your local materials source and tell them what you are doing. You need the gravel to pack enough to hold the hydrant in place well, but still allow water to evaporate out. I'd probably even cover the top of the bit with a layer of landscape cloth and then put a light layer of gravel on top of it.

Obviously, the larger the pit, the more buffer room you have before the water gets to too close to the surface. In winter, if that happens, then the water could freeze and transmit that cold downward ... causing problems.

Sometime this fall I need to rebuild our hydrant. We've been getting leaking around the rod that goes down into the hydrant. In winter that is the kiss of death. We bought a kit that comes with a new plunger and some other parts. I've seen a video on-line where you unscrew the top and pull the whole thing out from the hydrant and then replace that plunger. Looks easy enough. I hope we can do it.

BTW, our hydrant is inside our unheated horse barn. Just to play it safe, I ran a heat tape down the hydrant's main tube, wrapped it with insulation, and then covered the whole think with a length of that black corrugated drainage pipe that I slit down one side (so I could put it around the pipe). In really REALLY cold weather we'll turn on the heat tape. The corrugated pipe is to keep our barn cats from shredding the insulation or damaging the heat tape. Its worked so far. Nothing would be worse than having that hydrant freeze in the winter. That would be a ton of work hauling water to the horses.