1. Do a soil test (e.g. Logan Labs or UMASS soil lab) and amend the soil
accordingly. If you choose to do only one thing to your lawn, this is the
one you should do.
2. Adjust the irrigation system to do deep but infrequent watering. You
have cool season grass so you shouldn't be in a very hot location. The rule
of thumb is to water 1 inch (so water gets into 4-6 inch into the soil)
once every 7 days. Depending on your soil, you may need to adjust
accordingly. But every 2 days is too much.
3. You have thatch buildup, so the first thing coming to mind is mechanical
dethatching and aeration. This could be controversial but my advice is
strongly against mechanically disturbing the soil or you could get a lot
more weeds coming up. Instead, you should gradually add organic matter to
your lawn (e.g. top dressing with compost), and do liquid aeration (you can
search it on the web). Don't be discouraged by the pricey 'liquids'. If
you are interested, I can point you to a link teaching you to make it
yourself. This also answers enviro's question: Should you dig/till before
overseeding? No, you shouldn't.
4. (Optional) Switch from synthetic fertilizers to "organic" ones like
Milorganite. I quoted "organic" because it is debatable whether Milorganite
is organic (you can search it on the web). Although I am not sure whether
I would use it in the vegetable gardens myself, I have no problem using it
in the lawns or considering it "organic" for lawns.