Transistor as variable resistor in LFO
Your design is a simple phase shift oscillator that uses series R to control loop gain. 

Your requirements have 2 main parts; a triangle VCO or Pot control LFO, that has warble or jitter on the variable input included.  I will address part 1 using a transistor but you can use a Pot instead.

The latter must be BETTER defined more in terms of random frequency range and modulation or by sound byte example.



part 1.

Perhaps a better way is a simple Relaxation Oscillator to use shunt feedback to reduce amplitude at the virtual ground point so that voltage drop is a virtual AC null. (this is a key point)
 The series R regulation induces distortion from voltage drop at max R.

[My Example Simulation] 

I answered this already for a sine wave 10MHz VCO with a 4 or 5:1 tuning range which is a bit harder.

However, as Voltage bias decreases, impedance rises and voltage rectification occurs making the sine wave look somewhat like a full wave rectified at low frequency when R is limited by a shunt resistor.  The series R limits the VCO for max f.

Until you have design specs you cannot design anything well;
 F: max-min, tuning ratio,  VCO gain [MHz/V or kHz/V] VCO linearity, Vin range
 V: amplitude Vpp and DC offset and amplitude variation tolerance,
slew rate on amplitude changes vs df/dt,
THD: Max, Nominal sine .. or just a triangle   wave