I'm definitely impressed by your idea. Absolutely go for it! And as others here have posted, you shouldn't have any problems entering DCA first with a closing time of 10p, then hopping over to DL.
The west coast portion is actually the easy part, since all that separates the two parks is the esplanade. And I know many others have done MK to DL in a day, but I haven't heard of anyone try all 4 WDW parks before flying to DLR. For me, the east coast section sounds more challenging, but I'm guessing you have a pretty good plan for that.
Are you taking advantage of an EMH day to get an early start in one of the parks?
Good luck with the rest of your trip planning!
P.S. While entering
Disneyland today, the family behind me had just arrived from Japan. They were in Tokyo Disneyland that morning and were getting to Disneyland right at noon. Although the distance is much greater, the logistics of Tokyo Disneyland-and-Disneyland in one day are quite easy due to the international date line. I hadn't thought about trying that two-parks-in-one-day challenge until speaking with this family. Disney fans are pretty amazing.