https://reverb-res.cloudinary.com/image/upload/s--Or_7-p6K--...
Elk Echo Machine v3 (EM-3) from 1970
https://www.acontinuouslean.com/2013/12/02/secret-capitol-st...
If the only "digital" part of the circuit is the clock then couldn't you replace that with a quartz oscillator that you can wire an analog modulator for in order to get the switch timing for the capacitors banking the sound? Am I oversimplifying this?
If I'm at all correct than I would also say I don't know of any product that does so since it sort of sounds like it would be going full analog for the sake of going full analog and wouldn't affect the tone AFAIU but sounds like there's no technical reason it couldn't be done.
Lots of heads and carefully tuned feedback (possibly also across different heads adding phase changes) could help in that direction. It would sound interesting, though the resulting contraption would also be big, clunky and expensive.