My method in the past has always been to open my preferred chain's website and search 6 adults in 1 room.
On Marriott.com, that should
only return the two-bedroom suites at Residence Inn, TownePlace Suites, and any vacation clubs that happen to be in the area. It rarely pulls back anything else - even Presidential Suites in most hotels don't have bedding for 6.
If I don't like what I'm seeing with 6, I drop it to 5. That casts the net much wider - you get tons of two-queen + sofabed rooms, which is most SHS, some FI, and some 1-bedroom suites in other brands.
If I'm outside the U.S. where the suite brands aren't common, I'm more likely just to start the whole search at Booking.com or Airbnb and find whatever unit size I need there.
I will check out that Suiteness site. Sounds like a good resource.
The DC area is awash in Residence Inns. You'll be able to find a 2-br suite without too much trouble and it won't cost eight grand a night.

There should be HH or HY options too, but DC is a huge Marriott town so they're going to have the most options.