Perhaps muck some of the mud out, put down landscape fabric to slow down the mud from pumping up through the gravel, and lay gravel on top of that. It would need to be at least 3 or 4 inches, I would say.
Or, just sand on top. I have a combination - one area more smooth pea gravel, next to it more sand - I am still experimenting.
But one bit help is that section of the pen has a 2% slope, more or less, into a small channel that takes the dump water and splash down to a garden bed.
I did this in key areas, I laid down landscaping material[very important] or gravel will get incorporated into the mud, then I laid the river rock small round stones on top at about 2" deep. works great so far.