Having belatedly read The Secret Horsepower Race, apparently German engines were not getting the maximum boost possible out of their existing fuels (especially C3 but even B4) for most of the war due to those issues.
Main benefit of C2 was that it would not have reacted with fuel tank lining or got into the lubricating oil the way C3 initially did due to its different chemical composition. So the DB601N might actually have worked.