NAPS is generally for recruited athletes, racial minorities, and folks from underrepresented parts of the country who don’t currently meet academic requirements, as well as enlisted sailors. There are always exceptions but by my estimation around 95% of Napsters seem to come from these categories.
For someone with a very strong academic record, it’s unlikely you’d be considered for NAPS. Your biggest problem was not having a nomination for an appointment, so I’d start there. Perhaps you come from an extremely competitive district. Consider asking your congressperson’s academy co-ordinator how you can be more competitive.
The commonly cited prep scholar data is misleading for service academies: It’s giving you the average stats of appointees across the whole country, when really the competition is played out within each district. Therefore to make an accurate prediction you’d need admission statistics from within each district, which are not available. In some instances, a 29 ACT score could be good enough, while in others, a 34 merely gets your foot in the door. It’s frustrating but that’s the reality of Academy admissions. As in much of life, key parts of the process are based on factors beyond your control.