Hello Jessifi, it sounds like you have two issues:
1 Historical compaction
2 Contemporary flooding.
Until the second is sorted, you may be taking two steps forward and one back with mulching to encourage soil organisms (if they subsequently drown).
There are many cases of healing compaction with surface organic matter – in my case at Lower Farm in 1999, and here in 2013. But that was without any long term issues of lying water.
You may need to consider laying some drains, I would take advice on that.
