The famine in question (early ‘20s, not the later famine that resulted from de-kulakization) was made much worse because Lenin kept exporting food during it. The Bolsheviks did this because it was their only source of the foreign credit they needed to buy the machine tools and whatnot they needed to ramp up their industrial sector.

I really think you're mixing up the famines. Export of food to acquire industrial capital was a major motivation during the Holodomor. During the Russian Civil War, the motivation was to keep the Red Army fed and in the field without having to make concessions to the peasants, independent regions, or demobilizing any troops.

I wouldn’t call that “war communism”, just straight “communism” as per Marx they felt industrialization was everything.

War Communism is a reference to a specific set of policies adopted during the Russian Civil War.