I would have it refretted. You would have the option of having the frets done in a different style, i.e., like a Martin, with the nibs in the binding removed and the fret tang notched so the fret would extend over the binding. If the frets are really low, there's a chance the nibs have [previously] been dressed/leveled down enough you couldn't keep the nibs with different/taller wire anyway unless you had the binding replaced.
I would get more than one estimate and references for the work if you have any options. It's not rocket science.
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