I've seen a shim used to tilt the neck up slightly (not down like most shims) that made this problem quite a bit better, as long as the bridge had room to also bring the strings down to keep the action playable. Without it all the strings buzz from about the 5th fret up unless the action is set too high. Basically it makes the ski jump 'up-slope' flatter, ie closer to parallel with the body. Can be combined with putting in some fret fall-away. If the alternative is a re-fret or new neck then it can be a 'last ditch' option.