Yep, I used that second method of learning the E and A strings 1st (expanding and linking the fret markers as guideposts), and I especially agree about not concentrating on the sharps/flats.

As far as learning quickly, I'd guess after some proficiency has been gained to drill with cards or that trainer linked above. I'm guessing it's really similar, but there's this online trainer too.
And the website that was helpful with theory for me, has this lesson which pretty much covers what we said, but has some other good tips too: zentao.com