The misalignment might be the neck. Try slackening the strings, then loosen the neck screws maybe 1/4 turn, the bump the underside of the headstock with the heel of your hand. Don't try to force it, just a little nudge. There may be enough clearance in the neck pocket to align the strings. If so, just tighten the neck screws up and play. If it wants to slip back, you could put a shim the lower side of the neck pocket.
If longer intonation screws solve the reach problem, you're all set.