I have the same (or very similar) issue, just a little more to the back of my property. It's ok right now, but come spring or any rain it's muddsville. I live in SE Michigan, possibly in the same "basin" from way back ie clay
2 other options I've been looking into.
1) "Rain Gardens" - google it for your area. this is setting aside and maybe even lowering an area and planting plants that can use a lot of water when it happens.
2) adding supplements to help with drainage/improve drainage. This is probably more for surface clay, but adding gypsum, lime, organic matter can space out the clay enough to make it drainable. There are also other additives like humic and fulvic "acid" (read: acidic, not "acid that burns through steel" of course)
Though I'm also thinking about the post above about having a backhoe dig a hole, filling with gravel. But I'll probably DIY it because apparently I'm a masochist.