Answer: As you've discovered, growing turfgrass beneath maple trees is not usually successful. The grass has to deal with shade, but more importantly, the ground will be quite dry, regardless of your watering routine. The roots of maple trees compete for moisture and nutrients and by their shear volume, will usually out-compete the fibrous roots of turfgrass. Rather than trying to rejuvenate the lawn, why not grow a groundcover beneath your maple trees? Two that take foot traffic and dry shade include Vinca minor and Wintercreeper (Euonymus fortunei). You might also consider Bishop's Weed (Aegopodium), Heartleaf Bergenia, Lamium (dead nettle) or Redwood Sorrel for the site. If you have your heart set on growing lawn beneath your trees, you might try seeding with fine fescue, the most shade tolerant of all grass seeds.
Moss can be removed by raking (or you can apply moss killers, but you'll end up raking the dead moss out anyway). Once the moss and old, dead grass has been raked out, you can broadcast your grass seed.
Hope these suggestions are helpful!
Q&A Library Searching Tips