Hi Sam

The distortion you are hearing from the D string is almost certainly a piezo pickup issue in either that the piezo module is dying or the conection to the module is loose or otherwise damaged.  When removing strings it is necessary to trim off the coiled string end that has been wrapped around the machine head post otherwise this can snag on the fine wires that connect the piezo module to the electronics as you pull the string out of the rear of the guitar.  Nevertheless it seems that it's fairly common for the piezo modules to die across the Variax range.  I haven't experienced this yet on any of my Variaxes, but I have dealt with Line 6 UK Support on the phone regarding knobs for my Spider Valve, and the lady I spoke to was incredibly helpful and put a couple of knobs in the post which I got the next day.   Having seen reports from other people on these forums - specifically about piezo issues, the response has pretty much been the same across the board as far as I can see.  There's two ways to get this resolved: raise a support ticket here and your request will be forwarded to UK Support who will probably contact you by private message through your account here, by phone (as they did with me) or by email.  Replacing the piezo is fairly straightforward I understand so it is possible for you to do it yourself or to get the work done by an authorised repair centre/competent guitar technician - largely depends on your warranty I suppose.

HTH

Nick