You’ve piqued my interest. The Mod Delay algorithm could be useful here. The antiphase / out of phase MOD SHAPEs almost disguise the periodic waveforms. The lowpass filter can darken up the repeats. I don’t know how accurate this is, but I set the maximum delay time to 400 ms. (image below), and swept both delay times to a 40 ms. minimum with the expression pedal. For a little bit of analog-like pitch-shifting on a the delay sweep.
But what I really think you need here is irregular pitch modulation. I think that random speed & depth modulations would go a long way towards authenticity. And you can adjust how subtle – or extreme – those modulations will be. I uploaded an exaggerated example below, using the Vibrato algorithm. Adjust any upsteam delay unit to taste, then follow up the wet signal with sloshing oil. I programmed the expression pedal to reduce the Intensity to 25.