Flooding townhouse back yard
Looking for some advice here. Within the past year I moved into my current home, a center unit townhouse. Our row of townhouses was built poorly, so the ground slopes towards the house with nowhere to go, so it just pools there. Since I'm a center unit I can't divert the water to the sides. I have a constant issue of water pooling in my back yard for the first 24 hours after raining, and the ground remaining soaked for a good 4-5 days depending on the amount of rain. If it rains enough, water actually starts to seep into our 1st floor (ground level). I've searched pretty thoroughly but every drywell/French drain solution I see doesn't quite apply, so I'm looking for some advice anyone might have. Attached is a picture of our home, our fence line, and where the water pools/ground is soaked.
Idea 1 involves digging a hole at a 20 or so degree angle and putting pvc pipe in there with holes towards the bottom. Hopefully this would move the water from where it collects, to underground where the water isn't. This is my favorite idea since the ground near our fence line dries quickly and normally, so it isn't as saturated.
Idea 2 involves large drywells, like a flo-well, to just collect and hold the water. I worry these will fill up quickly with the amount of water our back yard gets. I also worry the ground there is already saturated, which is why the water is collecting there anyway.
Idea 3 involves the same thing as Idea 1, just straight down. The water will be in the same place, just able to get further underground. I again worry that the ground is already saturated there so this might not do much.
Thoughts? Experiences? Is this hopeless, or will one of those ideas work?