washing dirt off black fence

i used the ol' lexington tar/black fence paint for my deck trim railings (i went with horizontal 1x4s instead of lattice) and had cleared the grass around it in preparation to fill that area with rock.

well of course i didnt get the rock put in before i had a couple of monsoon rains and now the bottom 2 rails are completely covered in dirt splashed onto them.

now that i have the rock down i need to clean the railing.

a cursory wipe with soap/rag doesn't seem to do the job but i'm afraid a pressure washer will take the paint off.

any recommended cleaners or techniques to get these back to looking black again?

TIA