Noun or adjective phrase. An occurrence or situation that has happened or will happen only once. U.S. equivalent for the adjective is “one-time.” No U.S. equivalent for the noun. “The editors promise that Panorama is a one-off and not Volume One, No. 1 of a new publication.” (Bruce Weber, New York Times ArtsBeat blog, October 14, 2009)/”Friday, Michigan and Air Force announced a one-off game for the 2012 home opener in Ann Arbor.” (MSNBC.com, January 29, 2011) Google Ngram.
notoneoffbritishisms.com 
It seems like your rule would argue for a “Perfectly Fine” vote for the noun, and a “Over the Top” vote for the adjective.
The US equivalent for the noun is “one of a kind”.
In my younger British days in the Army and in “civvy street”, quantities of countable goods would commonly be ordered as “n off” rather than “n of”, as in “Helmets, tin, 1 off”; “Four-inch nails, six off”. No idea why, and it always bothered me. I suggest this may be the source.
Or a factory assembly line product of which only one manufacturing run is made.
“One off” seems completely natural to me and I’m Canadian. I don’t use it regularly, but I definitely have said it, and I’ve never thought of it as a Britishism. It must have come over the Atlantic before I was born.
“One time” seems to me to be a perfectly good American equivalent.
I came across an early ‘one-off’ the other day. In Sue Thomas F.B.Eye (ep 8?) two FBI agents are talking to a European shop owner about his customers, and he says something like ‘I had a repeat client and 5 one-offs’. The two agents looked puzzled and had to ask for a clarification. I think this was some time in 2002