The Tale of Years entry for SA2280 has:
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Umbar is made into a great fortress of Númenor.
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Of course the Numenoreans could have had strong places by the sea before then.
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The conjectural evidence still points heavily to a Númenórean rather than a Haradrim in the case of the sorcerous, necromantic WitchKing
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I don't disagree with the conjectural evidence, but consider: the text states that the Witch-king became a sorceror
after he recieved the Ring, not that he was one before:
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Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old.
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It hardly seems relevant whether or not he was from a culture steeped in sorcery before.
Likewise, he hardly needs to be long-lived. Bilbo was almost corrupted in just 60 years and he was a more resilient Hobbit, of good will, and who didn't use the Ring much, and these are the key deciding factors according to Gandalf (see above for the quote). The amount of time you have the Ring for isn't really what's important: Khamul as an Easterling wasn't long-lived either.
Speaking of Khamul, he was likely also a sorceror as a Ringwraith so if true that just serves to underline that prior culture is really unimportant.
As I said before, this is really just arguing the toss. I personally consider it most likely that the Witch-king actually was a Numenorean but it is interesting and informative to deconstruct something taken for granted.