I've only had two Variax guitars to work with, but so far I've run into the same situation with both, and wondered if anyone else had encountered it.
The nut is too close to the 1st fret, and the bridge is too close to the 12th fret. Now, I'm setting these up with light gauge strings (starting with a .008), and I'm setting the action at about 3/32 for the low string, and 2/32 for the high end (at the 12th fret). The height of the string over the first fret is okay (though that was kinda sporadic), and I can get strings 1 to 4 to intonate, but the saddles string 5 and 6 both bottom out, and that's with the set screws for the bridge posts at full extension.
So about the nut...even on properly intuned strings, the pitch of the fretted first fret is sharp (and I'm being very careful to only just lightly fret them when checking, so as to not stretch the string over the fret). What I've done to rectify the issue is that I've carefully filed the nut on the neck side with a combination of flat filing, and filing with a slight angle, so as to bring the contact back as much as 1/16" or abouts (I also filed the top down quite a bit, as the strings were set pretty deeply into the nut, and there was a lot of extra nut above them)...and for the bridge, rather than pulling the posts, and plugging and resetting them, I have temporarily used some longer set screws and pushed the posts out to just short of losing their widest contact.
It works, and it sounds much better now.
So has anyone else encountered this? Maybe Line 6 needs to check their jigs?
Ken