Interested to hear how OP does with this upgrade, please report back.
I've had great success in upgrading NH booked Z fares to first class on NH flights, NH ticket stock, as an AMC Plat and DIA.
OP was smart to ensure their flight wasn't a code share, as then upgrading I believe would be impossible via UA.
Also wonder if OP could transfer AMEX points to NH AMC and then upgrade the NH flight using NH miles. Not sure if that works on UA ticket stock and OP may need to use an AMC number for mileage accrual in that case, but I'm just guessing here...