UPDATE: We got linked by Speculist — check the comments, there’s an awesome link in there that I’m in the middle of trying to digest. Hopefully, it’ll pull in results.
How about 10 grand for somebody who can come up with an actual pedagogy or course based on Bodmer’s “The Loom of Language?” I don’t have it, but I could be persuaded to pony into it if other folks got on board…
I’d like to speak a dozen or so languages, and everybody I’ve ever met who can do this (particularly philologists from East-Central Europe), seem to use the exact same approach that’s suggested here: leverage skill in one language into an ability to get around on a basic level in every related language. So if you can read a paper in English, you can read a menu and at least a few headlines in the Scandinavian Germanic languages. Or so that if you can read good French, you can function on a survival level in the other romance languages (let alone the Slavic ones, all of which as close together as French is to Italian).
Assuming, then, that you speak one of the related languages, why not build up pattern-recognition exercises designed to make foreign but related vocabulary intelligible? It won’t get everything, of course, and false cognates would be an issue. However, being able to adjust from one’s native vocabulary for a given core of language would allow for survival-level communication, thus allowing a speaker to move around while focusing on the grammar, which is what will unlock newspapers, etcetera.
It would sure make that high-school language course worth investing in.