Thanks for checking back Andy.
I haven't actually tried raising the tailpiece yet, stupid busy, but I've been wondering if it has to do with the high E saddle.
I only hear the decaying fundamental thing on that one note on that one string, but I do hear a somewhat different and more pronounced set of high overtones everywhere on the high E, as opposed to the other strings. It's a different gauge of course, and nothing is the same as anything, but it made me wonder.
Do you think replacing that one saddle is worth a try?