Bats: most people do it wrong and get no bats. Cruise the net and make sure you do it absolutely the right way, or your efforts will be wasted.
Drainage: This can get into big expenses. Hmmmm .... If you could get a ditch witch in there and some drain tile and you had a place for the drainage to go .... Here's an idea: can you reshape the surface of your yard a bit? Make the center about an inch higher than the edges? That way, at the very least, water doesn't accumulate.
I was trying to think of an earthworm situation that could fix things, but it sounds like they would drown while hibernating.
Cedar: you can get things to grow, but cedar litter has a natural herbicide in it to make it so it doesn't have to compete with other plants. I generally just let cedars have their spot.
Grass variety: tall fescue! (not a mix)
Oak and Maple: the trees and the grass are competing for nutrients and water. I'm guessing that you have been raking the leaves? Are roots showing? Often, the trees (and grass) comsume lots of the goodies from the soil so the soil sort of shrinks. In nature, the tree litter (leaves and twigs) will replentish the soil. Same for grasses - although they typically take a trip through an animal first. If you want to see that spot spring back to life, you'll wanna find a way to get all that litter back to the soil. When some leaves have fallen, mow with a mulching mower - tiny leaf bits will wind their way between the grasses and feed the soil. Too much mulched leaves will mat and kill the grass. They would be better for
compost to come back the following year.
The ultimate: drainage trenches at least two feet deep. The trenches could then be refilled with earthworm habitat. The earthworms will hibernate there in the winter and work on making your soil deeper during the spring, summer and fall.