This has happened to all my fuzz face style builds (and the One Knob fuzz variants), using BC108/109...
The fact that the emitters are connected directly to ground sets it to maximum gain, this is obviously to much...
By adding a 100 Ohm (or a bit more) between emitter an ground (for Q1) or between the Fuzz pot's lug 1 and it's ground connection (Q2), you will prevent it from going to max gain and into oscillation.
Here's a second thought: Have you tried it with batteries or a different power-supply?
The reason I ask is that when using poorly filtered power-supplies, you sometimes can get oscillation with very high gain circuits.
This issue includes many of the "professional" power-supplies as well, like the horrible T-Rex units, and not just the cheap one-spot units.
Many of them only has just one regulator for all the 9V outputs and no decoupling/separation between the outputs, making it function just like a one-spot with a daisy chain.
This is why I mainly buy one-spots and build myself a one-input with multiple output power-filtering box, with a "Huminator" decoupling circuit for each outlet.
Here is a couple of forum links with information and layout regarding the Huminator:
http://guitar-fx-layouts.42897.x6.nabble.com/Bypass-bleeding-td33074.html;cid=1486678163399-94#a33084http://guitar-fx-layouts.42897.x6.nabble.com/Weird-quot-hum-quot-from-a-couple-of-pedals-td20501.html;cid=1486678163399-94#a20504