Cold starting an engine is very different from an air restart. Cold starts require sending fuel to the engine, setting the mixture for ground start, etc. While a ground start might take minutes, once the engine is started and the propeller is turning, restarting the engine is effortless. In reciprocating engines, it's just a matter of ensuring the fuel pump is on and the mixture is open. Restart is simply a matter of turning the key at that point and the power comes back almost instantaneously.
Unless you're suggesting a more complex ground start sequence (such as in DCS), there's nothing really to be fixed.