Traced this Kay Effector PCB layout from Google. Sorry it's a bit cramped.
I believe the op-amp is an MC1458, there is an unknown transistor in the LFO section that the PCB layout labels K9. I assume it's a PNP BJT just I can't say for certain. The speed pot is an unknown value though I assume it's similar to the one found in a Vox repeat percussion. Volume and tone values are also unknown, as well as the placement of the tone pot in the circuit though I assume it's on the volume pot input.
Worth noting that the 'Echo' switch takes its signal input from the other pickup to everything else in the circuit. The fuzz section is out of phase with the rest of the signal circuitry too.
There's clear room for improvement as there's a lot of resistor values that would significantly reduce the max output.
Rather suprised that this hasn't been documented before.