One possibility I considered was a “hat”. A PCB with male headers/jacks that exactly correspond to the panel that you push on top. This would only need the traces necessary to provide the jacks and would be completely non destructive. This poses a few problems that I can see. First of all: how do you access the pots? They could be make accessible directly, but once placed alongside full sized jacks this would be quite inconvenient. You may be able to add knob caps but I can’t really say for sure. Next would be visibility of LEDs; I don’t know that there are any on the panel, but the pots are illuminated and that conveys information you probably don’t want to lose. Finally it may be very hard to install. Getting a couple of rows of headers to line up is tricky enough: getting 50 disjoint header points plus the 5 ports to all line up at once seems very tricky, no matter how carefully you construct it (maybe it would be made in several pieces?).
You might be able to avoid this by having it stand off and installing a rat’s nest of wires in between, but at this point the type of break outs people have been discussing probably make more sense. I suppose you could make one that more closely matches the layout of the Volca and provides jacks for every patch point which you hook up with ribbons (lots of the patch points are in little groups, so it would make the wiring neater). Even then, all those connections would probably obscure the panel and make it hard to access the pots without a lot of careful routing. This also loses a lot of the charm of the device (compact and self contained).
All in all I think making a new case with all panel mounted controls and ports is the only way to end up with something that retains all the usability and consistency of the original. It might be a fun project for someone, but not something I’d be inclined to undertake.