Just a quick note to advise you folks that sometimes you help just by being here, without actually doing anything. I've been fighting a nasty little problem with JLayeredPane for six hours, and I finally gave up and searched here for any references to JLayeredPane that might help; no luck there. So I set to work writing up a proper question. In order to make the question clear, I had to carefully set up a simplified version of the code to present here and discuss all the variations I had tried. While doing so, another variation occurred to me; I tried it and lo! my problem was solved!
There's an old naval phrase "fleet in being". It refers to a fleet that sits in port and never does anything, but the mere fact that it exists creates all sorts of problems for a potential enemy, who must jump through lots of hoops to deal with the potential of that fleet, even though it never actually leaves port. You folks are sort of the "programming help" version of a "fleet in being".
Therefore, I thank you for being. You really did solve my problem for me!