I'm finished!  At least except for the actual sounds.  I haven't updated the sounds getting triggered by each button but I can always do that a bit later.  I found that a great option for a speaker is a speaker from a Dreamcast VMU.  I know that's completely random but I happened to have a dead one laying around and I found that the sound was pretty good.  I drilled two holes in the front of the controller and that seemed to be about perfect.

As for the controller, I had to cut out several of the plastic columns on the inside of the casing.  I managed to cut out enough that I could fit everything in.  It was a tight fit...

and here's right before I close it up

And here's the finished project

I had a really hard time getting everything to lay flat.  I used a lot of wiring to increase the amount of play I'd have when laying everything down and then used hot glue to keep things in place.  That seemed to work well but the battery just never seemed to fit.  After some work I managed to find a good way to close the case and not have it appear to be bowing around where the components were.  I'll plan on letting my son play with this tomorrow and I'll give an update on how he likes it.