Washington isn't significantly different then Adams or Jefferson, althouth the Cap Ridge route that you did is easier than any route to the other major peaks. On a nice day, Washington isn't any harder than those, and is somewhat easier since you have the summit buildings (food, water, shelter).
There will be lots of folks on any of the popular routes up Washington. Going past the hut isn't going to be any different than being on Tuckerman or Lions Head. You'll see somewhat fewer folks on Boott Spur, Nelson Crag, or Jewel. If you're worried about the length of the trip, you are probably best off taking one of the standard routes up from Pinkham or the Cog. You can do the trip from Ridge of the Caps, and you save 1000 feet of climbing, but at the expense of an extra 3-4 miles all above treeline.
The most important thing that makes this different from the other hikes you've done is it's a little bigger, a little longer, and if the weather turns bad, it'll be much worse. Get a good forecast, keep an eye on the weather while hiking, and turn around if the weather is getting worse. It won't get better as you go higher. The mountain will be there for another day. It's good to respect the mountain, but it's really not that different from the other peaks in the Presidentals. Common sense is still the most important thing.
-dave-