Okay, so my uninstall of the Visual Studio and SQL Server Betas didn’t go as well as I’d thought.  No problems on the VS side of things, but I’ll be damned if I could get SQL Express to install on my machine.  Luckily I found Aaron Stebner’s blog and his two posts (this and this) that outlined how to go about removing the remenant traces of the msi installations.  I followed the instructions and, voila, my next attempt at installation of SQL 2005 Express went just wonderfully.