Disclaimer/Suggestions:
I don't think these mods do everything that has been asked about the Moodring, but I did find them to be useful for making it quite a lot different than the stock build, way more into the ambient noise direction. Keeping T1 set lower seems to help a lot with the "white noise" issue I have read about. Perhaps ditching the Muff tone stack and going to the Rub-A-Dub Deluxe or Tenebrion style tone control would allow you to run it even lower for less hiss. Enjoy:

Starting at IC1A, an input level control, lifted straight from the Dirtbaby build doc, 1M will give some boost and grit, 500k is about unity gain at 95% rotation in my build, a hair of boost beyond that.
Next up, don't connect lug 3 of the dwell pot to the PCB pad 3, run a wire with a 1k5 resistor to the signal side of D3 and D4, now you have a delay line feedback loop as you'd find in a normal PT2399 delay circuit, yay! Don't forget to put a 47nf capacitor across lugs 1 and 3 of the pot.
Replace the Space pot with 25kB for longer delay times if you want, you can go 50kb but there will be a lot of PT2399 pssshhhhffffttt on the longest repeats. Also a good idea to put a 1k5 resistor between lug 3 of the pot and pad 3 of the PCB here.
Lastly, create a new "Dwell" control by building the little circuit between points A and B as shown. I built mine off the pot and shrink tubed it all together. This is lifted straight from the Tenebrion, which was lifted from CJ's Box-of-Hall IIRC. Makes a nice post-reverb buffered feedback loop, gets fun with droning self oscillation.