FWIW, the NJ result is the correct one on the physics; the error is in the language in 210.19(A)(1) and 215.2(A)(1).
OK, so the problem is bigger than just 210.19(A)(1) and 215.2(A)(1). The problem is that even though the definition of "ampacity" in Article 100 refers to the "conditions of use" and thus to a corrected and adjusted value, many sections like 210.19(A)(1)(a) and 215.2(A)(1)(a) use the term to refer to an unadjusted and uncorrected value straight from the table.
So if you interpret 334.80's limits on NM "ampacity" as referring only to rules that reference the adjusted and corrected values, it would apply only to 210.19(A)(1)(b) and 215.2(A)(1)(b), and not to the termination limits in 210.19(A)(1)(a) and 215.2(A)(1)(a). I.e. you'd get to use the 75C ampacity for termination checks, just like you get to use the 90C ampacity for ampacity adjustment and correction. 334.80 would still limit the actual current on #6 NM to 55A, which is not a problem for the application in the OP.
That's what the NJ interpretation should be saying (and maybe is trying to say, I only read it once). The proper way to fix this would be to be to stop overloading the word "ampacity" in the NEC and introduce a new term like "termination capacity" that is used in all the termination check language. Of course that requires looking at every use of the word "ampacity" in the NEC and determining which meaning is intended. And the writers of 334.80 could decide when they want to limit only the "ampacity" or also the "termination capacity". [Not a big fan of that term, would welcome other suggestions.]
Cheers, Wayne