I've got this on breadboard...

The transformer used is the old Eagle brand 200mW output transformer. These are the type found in those old Ge audio amplifiers that had stage coupling transformers. I've had some for ages (must have come from Maplins). You can still find them. This link has some data...
https://www.petervis.com/electronics/lt700-transformer/lt700-transformer.htmlA UK source...
https://www.cricklewoodelectronics.com/LT700-Miniature-Audio-Output-Transformer-1000-ohms-to-3.2-ohms-3.2-ohms.html...note that the description of these is often, and always has been, wrong. It only has one 3.2ohm secondary connection.
The idea is if the signal is large enough, the rectifier diodes keep working further into its decay. Even so, I used Schottky diodes for a bit more action. 1N5817 just because they were the only ones I had at the time. Using the transformer driven backwards by the secondary makes for a way-huge output amplitude.
To drive the low impedance winding, I chose a small power amp and that part is well known to everyone.
However, the load is still very low so a series resistance R2 was added and still has plenty of amplitude. This load would still be too much for opamps I think. Even with R2, it still needs the Zobel network R3/C5 to keep the amp stable.
The large 1000uF coupling capacitor should give response down to 100Hz. If bass isn't too important, the rectifier output still sounds good with a 220uF cap.
I added the Mode switch for direct amp distortion. I think it sounds nicer taken from the transformer drive.
The octave up works like you would expect with the same neck pickup bass tone input and note range as any other of its ilk. A clean octave blooms when the note decays closer to a sine wave. I don't think there's any getting away from that. However, you can play the solo from "Little Sister" if you like.
The part that I like a lot about it, is that with moderate input level and low amp drive, I can easily get ring modulator effects. I suppose it must be intermodulation distortion actually. Nevertheless, there are bell-like ring mod tones to be had, although not all intervals work nicely. Of course, you must sound at least two notes for this to work!
Has this been tried before - with the step-up transformer? I couldn't find an example. Surely it must have?