Wow that is such a cool project!
It is open source and it looks like a ton of code. Almost the entire project appears to be hand made.
I don't see any reason why this couldn't run on a WVR.
A few lines would have to be changed to setup the PCM5100 DAC vs the one that the drum computer is expecting.
It would be an interesting experiment to see if it could be modified to use the 8gb eMMC memory chip on WVR, and use the WEB UI to upload sounds. It is hard to say if that would work. On this drum computer the sounds are stored in flash, so they are much faster to load, but also much more limited in size, probably 1 or 2 MB total storage?
In order to test it you would need a usb-ftdi module, and use Arduino IDE to upload the code, and to upload the samples.
Then when you were done, you could flash the WVR firmware again.
It is also possible that the author would be interested to modify their project to operate inside the WVR framework, so it could live inside the firmware tab in the WEB UI. I expect this would be a fair bit of work, but, I suppose it couldn't hurt to ask them!