My watering schedule is twice a day for 15 minutes, I have a sprinkler system on a timer.

Two things about that: first, I'm surprised your grass does not look MUCH worse. Here is a picture of the difference between daily watering and weekly watering. The lawn on the right gets watered deeply once per week. The rest of the lawns get watered every day. Picture was taken in July several years ago in eastern PA not that far from you.

Thanks to morpheuspa for posting the picture.

Secondly, weed seeds need continual soil moisture to germinate. When you water twice a day you are providing continual soil moisture. If you water once per week, the soil has a chance to dry out completely between waterings.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, oscillator sprinkler (full sweep) and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and for the most part, in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

Having said that, if you decide to alter your watering schedule, you cannot go cold turkey from twice a day to once every 2 weeks or week. You will have to wean your lawn's roots. Currently they are extremely short because they can be. They "know" they are going to be watered in a few hours. As you stretch out the watering interval by days, the roots will have to grow deeper to get moisture. If you are deep watering, then the water will be there deeper in the soil.

Another consideration is your soil might not accept a long interval of watering leading to runoff. If you start to water and get some runoff, stop watering immediately and let the water soak in for 15 to 30 minutes. Then resume watering. If you get more runoff, continue pausing as needed to let the water soak in.

If you still have some of these weeds in late Sept, you could use RoundUp to spot kill them and reseed with TTTF seed.