I have clay subsoil as well. When clay is saturated, it takes a loooong time for water to drain through. This makes it a fantastic filtering medium, but can also cause drainage problems in wet years.

Is the dampness causing problems? If it's only a nuisance issue, it may be enough to put down a layer of gravel and sand on the surface.

How deep is the valve assembly? It seems to me that moving the drain outlet to a deeper sand/gravel filled pit may help. This is simply a holding area for the drain water while the clay slowly absorbs the moisture.

The other part, I suppose, is to use the hydrant in a way that minimizes the number of drain cycles. For example, installing a small above-ground tank for the frost-free season may be a good idea. Or, for the summer, leave the main valve "on" and add an above-ground tap to shut off the flow.

My 2c.

EDIT: Ken's evaporation pit idea is interesting. Hadn't thought of that. It explains the sewage mounds that are required for areas with low drainage rates.