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.