In our office, after much tearing out of hair, we had also discovered, like "bryanbowers" above, that the Layers panel drives the reading order, even over the Articles panel. I suspect that just reordering all of my content just using the Layers panel is the only thing I need to do to ensure that the reading order behaves, over the Articles panel, over the Structure Window, anything else.
There is one annoying exception (and if you can get along with this, then things do work). The PDF that we save out as a 508-compliant file is layered, similar to your original InDesign file. And because the reading order works by reading the bottom layers first, any background layers will be read first, no matter what, and cannot be moved around in the Reading Order panel in your exported PDF (unless they're tagged as Artifacts and not read at all).
Think of this as the same as in a Photoshop layered document. If you move the bottom layer in a Photoshop file to the top, everything else disappears behind it. Well, it's the same as for your InDesign Layer panel and your exported 508 PDF. Background images must stay in the background, and will be read before any overlays or labeling, unless they're Artifacts.
I hope this isn't too convoluted. I just thought this was a nice discovery. And it's pretty simple, once you work with Layers. It's simplified our production a lot.
So, conclusion: Reorder the Layers panel content in reverse order of how you'd like your reading order to work in your PDF.
