You are right that removing the nitrogen from the oxygen source would remove most of the NOx compounds from the exhaust. Unfortunately, switching to a pure oxygen feed, regardless of the source of the feed, leads to a lot of additional problems that would need to be engineered out of the engine. The "inert" nitrogen in the air is doing far more than providing undesired side-reactions - it is also diluting the gasoline and oxygen to the point where you get a controlled burn rather than an explosion, and carrying a lot of heat out of the engine so the rest of the cooling system can keep up. Pure oxygen is also an extremely corrosive atmosphere, and you could easily end up igniting the metal in the engine as well as the fuel, especially if it is an aluminum or magnesium containing alloy.
So your first step would need to be designing an engine that could run for ~100,000 miles, whether it was operated 12 hours daily or only 1 hour/week, on a pure oxygen/fuel mixture. Then you can worry about the source of pure oxygen.