What is a different way to spell "harmony" to make it unique?
You might try:
harmonie, the Middle English (e.g. Milton) spelling;
armonye, Chaucer's Old English version.
Neither of these could truly be considered unique however.
Perhaps you could use wharmony (with the "w" used as in "who") or harmoney (an incorrect spelling, but probably unique) or pymnea (with an explanation that it's some kind of non-phonetic, regional variation, pronounced as "harmony").
All of this (of course) raises the question of why you are trying to find a unique spelling. What purpose are you attempting to fulfill?