Everyone mentioned most of the usual tricks, but one.
To get your sticky typewriter keys working again, while you're flushing out the segment with your solvent of choice (lacquer thinner, paint thinner, mineral spirits, alcohol, etc.), actually move the typebars using the keys or by other means. This will help to get them moving and allow the solvent and subsequently compressed air to help flush the oil, dust, hair, etc. out of your machine. You've already got a mechanical cleaning device of sorts (the typebar itself) inside the segment, so move it while you're flushing it out!
It may take a few repeated treatments/attempts to get it all clear for all the keys, but it's far easier than taking everything apart.
reply to u/nogaesallowed at https://www.reddit.com/r/typewriters/comments/1cp75ln/how_do_you_clean_a_1mm_gap/
People were recommending all sorts of ideas and solvents here, including folded card stock, tooth brushes, floss, toothpicks, interdental brushes, wood cuticle sticks, Swiss Army knife tweezers, microbrushes, and even an ultrasonic cleaner.