Try blocking the trem when intonating. Cut some wood to fit both behind and in front of the
trem block to keep it balanced in the center position (the position you have it set for normal tuning).
As you change the position of the saddle(s) you change the tension and this can cause the bridge, at full tune, to go up and down a bit in balance.
So, you intonate the sixth string perfectly, then intonate all the other perfectly, and some of the strings end up off as the bridge goes up and down a bit.
True, this shouldn't be a big difference, but if you have to move all of your saddles back, or forward quite a bit it can really change the angle of the bridge to the point that you'll have to adjust the screws to compensate, thus changing your intonation slightly.
With the bridge blocked in a neutral position, all you have to worry about is setting the intonation, and when all six/seven strings are all set, you take out the blocks and adjust the claw to bring everything back to "center".
Just a thought,
Mic