No matter where you put the adverb, it makes a simple declarative sentence into an ageist slur.
Could the "director is not young unfortunately" not be accepted? It sounds and actually is more correct.
I would actually start the sentence with "unfortunately". Or put it at the end like you. But not in the middle, I agree. Yes, those should be accepted.
At the beginning or the middle sounds better to me than at the end. (And at the beginning or end, it needs a comma, I think.)
I also think it sounds best at the beginning or middle. I do, however, think it sounds okay at the end if you place a comma before it, as you mentioned. I don't believe I would likely use a comma when placing it at the beginning, but that certainly doesn't mean it sounds odd that way; that's simply my preference.
All of what I said above is simply what I think. ^_^