I finally managed to get this figured out.  The final steps came from Darcey Lloyd’s helpful video (thanks Darcey.  You rock!):
Darcey’s Video

. . . which inspired a web search . . . which turned up this list of steps:
http://alternativaplatform.com/en/support/setup/

Yes I’m working on Away3D Broomstick.  Gosh that’d be so cool to have a fullproof set of steps to get the code compiling in Flash Builder like those Alternativa guys have.  I know we’re still Alpha here.  Just saying.

The other thing to note was all of the errors thrown by Away3D in the Demo files downloaded form this site.  Someone on the web had posted that renaming calls to Loader3D.parseData() to Loader3D.loadData() . . . and moving the 3rd argument to the second spot . . . gets some of the broken demos working.

I hope this helps someone else to get Away3D working for Flash 11.  It’s pretty darn amazing, after all.

Special thanks to the Away3D team for all of their hard work.