If you are mulching the leaves and they are not being consumed by the micro-organisms, you probably have a low calcium level in the soil. Look for dead plant residues. Grass will grow under the oak trees, provided that there is adequate sunlite. Moss needs three things to survive, shade, poor soil and moisture, remove two of those things and the moss will die. You have improved the sunlite, now work on the soil fertility. Do a soil test, Check the calcium/magnesium saturation and adjust accordingly. Calcium 60% minimum and Magnesium 15% maximum Then apply the fertilizer's. If you dont get the calcium and magnesium levels right you are just wasteing fertilizers. You will also find that once you get the calcium/magnesium levels right, the moisture and compaction issue's will probably also be solved.