The Post Meridian Players put on a live performance of the original audio drama "Doctor Who and the Starship in Madness" where the good doctor meets H.P. Lovecraft and fights frog people. It was recorded live at the Arisia convention earlier this year and you can now listen to the drama (and watch the performers) online.
Here's how they describe it:
Suffering Shoggoths! The Roaring Twenties have just begun! Flappers! Gin joints! Deep Ones? The Doctor joins forces with H.P. Lovecraft to investigate attacks in Boston by monstrous entities, and the eccentric Professor Whiteman who appears to be behind it all! What is the secret of the Professor’s amazing chair that can seemingly cure the insane? What is “Miskatonic University”? What will happen to the world when C’thulhu rises?
And here's the video/audio: