I had an issue with the D string sounding normal and all working OK through an amp when the variax brain was off, but no sound when variax brain was powered on. 1 string only. Similar symptoms as explained above. I think the problem ended up being too much string wound around the top winder after throwing on a new set of strings. The irony was that it came with no string wound around the top peg, just used the screw underneath to keep it in place. I was forced to put new strings on after accidentally bumping that screw which is why I wanted to wind more string on.
I also toyed with the grub screes to try and lower the action as part of the restring and found when too low it also contributed to the problem.
I guess the variax brain relies on more than pickups and these 2 things were what I changed from the default config. It seems to be working OK for now and countn't seem to find any workshop manual explaining best practices for when restringing and adjusting the action specific to the variax.