I opened up my Radio Shack "Electronic Reverb Control" delay unit and replaced jumper JP3 (which is in series with the original "delay" fader) with a 1MΩ variable potentiometer, as well as a 100kΩ pot instead of R21, which is the feedback resistor for the delay circuit opamp.

In the video I am running my Korg MS-10's output into the (noisy, but beefy) unit's microphone input and play a few notes. The larger knob at the top is the extended delay time, and the smaller knob underneath affects the feedback.

I captured the output with my soundcard, but applied no processing to the audio.

For reference, I used the following tutorials as inspiration:

https://forum.ableton.com/viewtopic.php?p=426956&sid=8d60bdcdd0f2933aa8a5ce3da7650b8f#p426956

and

http://clacktronics.co.uk/2011/realistic-reverb-noismaking-mods.html