Some machines in the running were the Empire Aristocrat, Olympia SF, and Scheidegger Princess-Matic.
But in the end, I'm taking a Groma Kolibri.
My flattest typewriter of all is this Gromina:
Why didn't I take it? Because it has a German keyboard and because the Kolibri has a more satisfying and effective mechanism. Notice the much flatter typebasket and segment on the Gromina, made possible by a clever geared-typebar mechanism. Clever, but not as strong or fast as the completely different mechanism on the Kolibri.
Stay tuned for some Kolibri typecasts from London.