Well, I think the connection is to do with something being surprisingly true, in particular with reference to time.
still: It's surprising that it's true now; we would have expected it to be no longer true.
yet: We are surprised that it is true now; we expected it to be true in the future.
even: We are surprised that it is true to the extent that it currently is. We expected it to be true, but to a lesser extent.
Note that I think "even" is more usually translated with the expression "til og med" - the picture here is "everything up to and including..."