Excellent info in posts #8 & #9. Good compost isn't fully broken down but needs the process to continue. Applied in spring, it can be difficult to keep action going when it dries out for summer. I wouldn't just top dress, but disc/drag it in to prevent a 'barrier line' between new/existing bases.
Two biggest mowing mistakes are cutting too short and not regularly enuf, not that the OP is one of them. When we cut 'down to brown' at long intervals different species race to recover their 'green' at different rates, so mowing 'long'-ish and on a schedule should keep height more even between cuttings. Bare spots fill in quicker and weeds are choked out. Soil is shielded/shaded from evaporation, sun-baked ground. Insects and wind-blown seed (weeds) will be somewhat taken care of by insects vs turf digging vermin or moles that feed on grubs more easily laid in exposed soil. Best mowing practice reduces other chores, period. (patching, watering, spraying).
We transplant shrubs/trees best during a month with an 'r' in it, so fall planting/overseeding has the best chance of success due to lowered watering reqs and more time to establish root system before a dry season. Don't ever bag unless needed to mulch raised beds, etc. Turf will build over successive seasons as clippings add compostable fodder and further shield soil. ("Mistakes will really set you back.") Fertilizer is useless unless proper Ph allows nitrogen absorption. Beer/water mix in spray tank will break thatch down in moist springtime conditions vs raking. 'Cool season' grasses (blues, ryes, fescues) will grow either roots or blades according to nitrogen access, light, and temps above freezing.
btw: Grass is easy on my sand dune in central MI, and foods plots here are tough by comparison. Recovering the worst areas (~1/2 ac sections) begins with spot spraying, frequent light fertilizer apps in spring/fall (minimizes soak-thru, waste, runoff into pond) until turf builds up. Seed/overseed in the fall and water-in to establish soil contact. btw: 'Contractor' mixes exceed because they blend durable 'bunch'-types with rhizomes that fill in weak spots and gradually replace quick-starting 'annuals' in the mix. Sure helps not to over-think it.
