I'm not sure at all what you're dealing with, but my first idea would be to find a way to use it as it is or with minor modifications. Perhaps plant something like willow or bamboo that is water tolerant, build a little pond, or alternatively create ridges that rise above the boggy area but that can take advantage of the water.
Throughout much of the US Midwest a lot of agricultural fields were drained using field tile; back in the day it was clay tiles and today they use a special plastic pipe that has holes in it. There is a special shovel called a tile shovel or tile Spade that is long and narrow just for digging trenches to bury things like this.
Feedback has been fantastic , thank you.
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You can still see fields in England and persumably in Ireland too where they have ploughed up and down the field creating what is called ridge and farrow lines which are off contour. They tend to be pasture fields now and sometimes people plant trees on the ridge and the excess water collects and drains in the farrow. If Seimi could plough in a load of biochar at the same time with a horse (to minimise compaction) he would be increasing the water holding capacity and forming the earth works at the same time.
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