I think that NH only recognizes Resident licenses from the states that it has reciprocity. I know that is the reason that my FL NR license is no good in NH.
Easiest thing is to get a NH non-res, PA recognizes the NH non-res. That being said there is a push from the city of brotherly love to end this, of course this will solve all of Philly's problems! Yeah like when O becomes a true American.
Like others said, NH's reciprocity only extends to resident licenses of reciprocal states. Get a NH non-res. It's only barely more paperwork than the PA one.