I agree with the post to keep it natural, let Mother Nature maintain it. My ancestors moved into the Appalachian Mountains in the 1830s and we are still here living among the trees. A forester suggested I remove several trees and in five years I would have more shade with healthier trees. He was right! I am no expert but I do suspect you have too many trees to maintain a healthy crop. A good forester could mark what trees to remove to maintain a healthier forest, with fewer trees to trim around, and have more shade. Also, you can mow the weeds/leaves and it should look as good as grass without all the expense of grass. Good luck and remember to maintain it to make you happy, not others.