I had a similar spot on the road I just finished. I contoured the road, crowning it and ditching so the water flowed to the pipe inlet. At the inlet, I dug a basin in front of the pipe to catch the water. Then I covered the inlet of the pipe with a heavy plastic milk crate, and filled the basin with stone. I put baseball size stone in the bottom and clean 57's on top. So far it's working great and i can drive right on top of the stone-filled basin. However, it will only take on so much water. But, in my case it's more than adequate for the run off.
You definitely need to find a good source for stone. My little road is only 300 feet long, and it took 160 tons of stone.
Based on all that soft mud, I highly recommend geotextile before stoning. Else, your stone will disappear into the mud pretty quickly. I used geotextile. While it's hard to get saturated ground around here right now we, during several days of steady rain intermixed with downpours, I have no standing water anywhere. The water just seems to disappear into the road while it stays good and hard. The drain pipe is working good too. We'll see how it goes when late winter saturation sets in next year. But, I'm pretty confident that with the crowning and geotextile, it'll hold up very well.