all the NSS does is complete the ground circuit to the starter relay, allowing the relay to energize the starter circuit.
if it starts in neutral but not in park, the switch is good.
that leaves only the linkage adjustment or the rooster comb as problem areas to address.
the NSS may need to be tightened a little more, or the wiring inspected to be sure the shift linkage is not inadvertently "moving" the plug a little. that tidbit cost me more than a few hairs to be lost before discovering that.