I would simply dig a gravel drainage ditch/french drain, covered back to grass on top, along the tree lines where the water comes from. This will redirect the water. Also on a very dry day rent a Yoemans key line plow, making full width zig zags down the slope(Use tapo maps to understand your contour pattern). Plant willows and may flag in the lowest spots. Your drainage can flow towards a pond if desired or just left channeled away. Keep the ground in cover crop, white clover paths. Plant your crops along the keylines.
