gram-inches sounds like mass x distance to me, not force x distance, (S.I. units being kind enough to distinguish between force and mass).
Whereas inch-ounces could be distance x mass or distance x force, as the Imperial system somewhat unhelpfully blurs the line between force and mass.
I don't know much about balancing rotating machines though, so where to go from here I have no idea....
Standing by to be corrected!
pb