For the string to neck alignment issue - I would dowel the existing holes and re-drill. This is the best solution and it won't look too bad as the bridge hardware will cover the dowels. Whilst you're at it, what is the e strings spacing like at the nut? If they are not aligned there it would be worth making adjustments to the nut now rather than later.
For the string height - yes, shimming the neck is the way to go. I had to do this on my RC-1 and it was a simple case cutting and graduating enough material to both raise the neck and adjust the break angle.
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