To my knowledge there isn't any hardware solution (at least simple) for APE files. You could do like suggested by the other poster and setup a PDA, but like you mentioned that may be too complex (plus costly). FWIW, I have tried the PDA route for both movies and music using Mainlobby frontend
http://www.webpromotion.com/cinemar/index.htmlbut that leaves a lot to be desired unless you use a tablet, primarily due to battery time..etc. If you had a TV set nearby that could be used you could setup a simple front end on that and use a regular remote control using software like Hairstyle within MC 9 (free), Mainlobby (commercial software), or myHTPC (free)
http://myhtpc.net/ to show the playlist and control buttons. Unfortunately, these options require a computer connection so you may not want to do that.
You could also keep the APE files as your "source" library and convert to MP3 or WMA files for use on a hardware solution like you linked above but that isn't very elegant way either.
Like everything with the Audio/Video interface to computers, nothing is simple.