In an act of desparation, I sent an email to James Knowlson, author of an aclaimed Samuel Beckett biography and founder of the Beckett International Foundation, asking if he knew of any recordings of Beckett's voice. Much to my surprise, he wrote back the next day. There's a recording of Beckett reading his story, "Lessness," but you can only listen to it (not copy it) at the above foundation, which is in Reading, UK. He also said there were some other recordings, but they're in private hands. So, basically, there's recordings, but I either can't hear them or I'd have to travel all the way to England to hear them.
That can't be all there is, can it?