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Is it this way for the entire length or worse at higher frets?
You say when you play it goes off, is it off unfretted or is it just very close? How does it compare with the low-E?
Sorry to ask so many questions, but it is hard to understand the exact issue. Vintage bridges have a much wider spacing so if you aren't used to them the strings do seem very close to the edge. (forgive me if you know this).
The other possibility is the neck can shift slightly due to an impact or whatever, meaning that the neck could be angled slightly, in the plane of the body, but away from the Low-E (downward) thereby causing the high-E to get too close to the edge of the fretboard.
If high-E and low-E are equally far from the edge at the nut, but very different at the higher frets, I'd say it was that the neck angle had shifted. Which in this case loosening the bolts a bit and shifting it back is the fix.
More information would help.
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