Need help designing and implementing an op-amp based distortion circuit
Your GND which is made by voltage division to 4,5V halves is weak, the first pulse throws it off from the midpoint of your 9V. The output clipper shouldn't be connected to it. Make more stable GND with an opamp voltage follower. Use the resistor-halved version only for opamp signal inputs. In addition reduce RG1 and RG2 to smaller resistances, say 47kOhm to recover from minor unsymmetry faster.

The signal input is now connected nearly directly to the output of the opamp through the signal source. That's positive feedback. The operation is very difficult to predict, because the input also gets signal and noise. I guess the guitar pickup works as resonant circuit and you have an oscillator.

Make a simulation where those points which are connected to your resistor halved GND are connected to each other with a wire and let the simulation GND be the minus pole of your battery. The resulted output is quite different than a perfect output plus 4,5V DC offset.