Another newb here.
My experience with this comes from Les Pauls. A lot of you covered some variables that I have not even considered,
but here is my experience.
With most Les Pauls, if you have the tailpiece screwed all the way down to the wood, the strings are stiffer and the tone tends to be a bit harsher and brighter. Now, when you start to raise the tailpiece, the action gets slinkier, easier to play. In addition to that, the tone softens and gets an almost "airy" tone; very nice. Notes just kind of bloom as well.
Kind of like you found out with your discovery, I think a lot of it came from the change in the break angle over the bridge.
String length may have something to do with it, but that is out of my realm of knowledge.
On a Les Paul, I would think that the amount of overall string length just by raising the tailpiece would be rather small, but it may be a factor in the slinky action.
Just my 2¢.