Well, I gave it a shot and it seems okay! I don’t think it’s a permanent solution but the spot is a lot less offensive and it sure was cheap and not that hard.
I scraped off the gushiest layer of the mud and then decided since I was playing with mud anyway to dig sort of a trench and build a mini berm to help with the overall drainage. I mixed in the bag of concrete (with my hands in garden gloves) as I moved it all around and then worked in the last of the bag on the new flattish surface. Then I misted the whole thing with the hose and roped it off for the sunny afternoon.
This morning it’s definitely not a rock but it does seem much firmer and although horses had walked over it the dirt held its shape pretty well. Boss Lady Mare still wants to pee there so I dragged over a mat to further dissuade her for a few days which will help with compaction I think. I am sure I will still end up dumping gravel or something there but I’m curious to see how it does after the next rain first.