A followup.  I called MSDN support on this one, and they said, effectively, they have no plans on fixing this problem.

Here's what it boils down to:  All alpha blending is down using filters.  Filters are only applied to on-screen media, not print.  And IE doesn't support the alpha channel in PNGs natively (or any other format, apparently), despite the numerous requests for it.

Thank you, Microsoft, for making my day a lot harder.