John, I did think of that, but diusmissed it because of the extra weight and complexity. My backup will a Co2 tank with regulator.
Caterpillar, John Deer, Waukesha, and others who used pony motors used them as the actual starting motor with a bendix drive. The cooling systems between the large and small engines were shared, that helped warm the big one for easier starting.
Many of the very very large diesel engines from early on, and perhaps still today, use a second independent small engine to run an air compressor just as you describe. This air would either be used with an air starter, or often dirrectly injected into the engine cylinder through a deticated air starting valve, turning the engine over and starting it.