Just wanted to report back. We ended up with a Junior Suite connected to a double room at the Park Hyatt, which we were VERY happy with.
PLUSES: kids loved and used the pool, beds were very comfortable, housekeeping service was good (room always felt very clean and all amenities we needed were there), plenty of space, even in the double room - we were able to eat room service for all 5 of us in either room! Hotel confirmed the room configuration we wanted by phone several days before arrival, despite it not showing as available online or when we booked. Guest services was quite helpful, including arranging a car service to pick us up at airport.
MINUSES: breakfast was uninspired, and no buffet breakfast available

And despite someone on FT saying the location wasn't great, we thought it was perfect. Easily walkable to many restaurants, Dupont Circle and the White House / National Mall. We walked some days and Ubered others. Hotel has a complimentary car service as well, but we didn't try to use it as it only takes 4 passengers and we're a family of 5.

Definitely not a high end luxury hotel, but we were super satisfied with it feeling exclusive and comfortable for the price we paid (around $300/room or less).