I have to read this in full but I have had two different bikes with low-speed frame shimmy and it made things miserable. One was a stock Bruce Gordon (have to look up the model) and the other was a custom Independent Frames touring bike.
Both had low-speed and moderate speed top tube (or so it seemed) shimmy. I tried all sorts of loading changes to no avail. And ended up having to ride without the handlebar bag on both to alleviate it a little bit.
I was wondering if it had something to do with my "geometry" combined with bike geometry. I thought it would be alleviated with a custom bike but nope.
I'm about to start shopping around for a new touring bike (the first was gutted for the second and the second was stolen) and I'm super gun shy and don't even know how to explain the problem to anyone as in the past they've usually said that they've never heard of low speed shimmy.
I will be keeping tabs on this topic!