Thanks to some tips from Pingnak over at the Kirupa forums, I have my .pngs loading in with alpha transparency intact.

I am still not sure why this was happening, but something about embedding the .png in the flash movie at compile time and then immediately using it to flood-fill the graphics layers caused the alpha channel to be ignored. Even when I embedded the .png, then copied the bitmapdata to a new bitmap, then used the new bitmap to fill the sprite, the alpha channel was ignored. I thought it might be the .png itself (which I had created in The Gimp), but when I looked at the png in any other setting everything was as it should be.

So I switched over to loading it at run-time (which is how it will ultimately be handled anyway), and everything seems to be working!

Now that I have this issue resolved, I am going to play around with graphics for different types of objects, and how to make sure the edges "fill" the offset areas so they look like full depth instead of layers.