If the class of service is sold out, no one can help - this is the first part of the problem.

If the class of service is available, then the fare rules will state whether or not there is a carrier plating restriction - if NH has one on this fare, no one can help...and such a restriction is NH's doing, not UA.

If there is no carrier plating restriction, a TA should be able to force the ticket on 016 stock, but that is something they need to try for you - only a test in the absence of a written carrier plating restriction would be certain...but a UA agent is not going to do this, only a TA will.