Hmmm, city onsen aren't like those linked to inns out in the boonies. I've already listed all those I know about with overnight facilities.

Here's a list and map (scroll down) of baths (not all are onsen) in the Ota ward
http://www.ota1010.com/yu.cgi?code=e
If I see anything appropriate I'll let you know - but you have all the information I have on this area.

- Sakurakann seems to be open until 1am http://www.ota1010.com/yu.cgi?no=050,code=e - but that's a bit tricky to get to
Sachinoyu has a 6am opening time http://www.ota1010.com/yu.cgi?no=007,code=e
Sachinoyu should be easy to get to from Haneda and both have onsen options in their range of baths

I guess you could stay around Kamata that night. Easiest way to get there would probably be Keikyu Kamata station (6 minutes from the airport on the Keikyu Airport line) and then walk across to the area around the main JR Kamata station. If you base yourself in Kamata then there's easier access to somewhere like Sakurakann or this unfortunately named onsen: http://www.ota1010.com/yu.cgi?no=011,code=e which might be my choice but closes at 24:00 or the recently rennovated Kaisei yu which closes at 24:30 and also looks appealing http://www.ota1010.com/yu.cgi?no=018,code=e.
In the between time there are a few modest "Love Hotels" around the main Kamata station where you can sleep for 3 or 4 hours (should cost no more than 5,000 or 6,000 yen but could be less if it's for the minimum "rest" period" (not an option I'd recommend on a Friday or Saturday night when the demand is highest). and there'll be some bars and izakaya open late.
Otherwise there's a Mitsui Garden, Vista Hotel and other more conventional lodging options in the vicinity. Jib71 has found the Kamata equivalent to a Dormy Inn and listed it in the post below.

Sorry I haven't got anything wonderful to suggest.