EmilyB the rare earth magnets are available at both Lee Valley and House of Tools. They come in a few sizes and the idea is intriguing. One would need a metal plate encased in plastic/silicon for the inside...and the outside magnets could be set in plastic...
I use these magnets in my shop to hold dust colection things together and they are powerful. I am assuming the felt is for the outside ... for the inside could you use the 3M green scouring pads? I just might have to try that...
:?