That being said it's still not a convincing argument that more men die from war than women die from child birth. The Mongols also administered a massive empire with a massive chunk of the Eurasian population. It was said you could walk from one end of the Mongol Empire to the other with a gold plate on your head and never fear for your life or belongings. That period lasted for decades...
I think for your position to have any merit you'll need to refute my point that (let's use the numbers you gave of 2-4 billion female deaths from childbirth) over the total span of humanity more people have died from childbirth than war