Use the Firebase libraries rather than the REST one to efficiently handle requests. I believe it uses a websocket internally. "It does all the work for you and is awesome." to quote Nick.
EDIT: After having played with the JS SDK a bit I'd like to add that it is indeed incredibly awesome.
I think it's even easier now that JS is a supported app language.
With access to a Firebase SDK the only major additions the API needs to become a viable replacement for existing read-only client apps would be support for all the other lists apart from top stories (new, show, show new, ask, jobs, best, active) and more than 100 items for each. For apps that need write access I'd suggest keeping the current website on a separate subdomain until that is implemented into the API.