I put this together this afternoon, only to have the same problem. I noticed that it got louder when my hand touched the sleeve of the guitar input, ie ground. I tried a few things that didn't work and then started poking around with a 2.4k resistor, circuit bending style. I had one end on the bottom ground strip, and I slipped from pin 3 to the anode of the horizontal diode, which did the trick without any contact with my body. Soldered it, and now it works fine. Not the prettiest thing, but it at least got the job done. Since it's on the underside of the board, I have a piece of double sided insulating tape between the resistor and the board.
Tl;dr, got it to work with a 2.4k resistor between ground and the anode of the horizontal diode.
By the way, I'm using two TL072's, two 1N4148's, a J113, and a 1M pot. I hear a whine in the background, but it doesn't seem as pronounced as what other people have mentioned. Hope this helps!