I have the same issue, but it cropped up when I had had the guitar for about 2 months. The is a ringing feedback type noise that comes from the low E which is pretty annoying, but there are also clearly 2 tones coming from the high E and, to a lesser degree, the other two unwound strings in the alt tunings you have detailed and others.
Could you go into more detail about how to readjust my hand (no palm muting, continually mute the low E with left thumb?).
I bought the Variax for 3 reasons, the alt tunings, the guitar modeling and the tremolo bar. I loved it until this problem cropped up. It seems that we are the only two JT 69 players that have noticed this. For me, it makes the guitar unplayable in all but standard tuning, drop D and open A. I'm going to reflash the guitar several more times and, if the problem remains, open a repair ticket and see if they'll fix or replace the guitar. If it can't be fixed, $1000 will go a long ways towards replacements, I think.