Since zombies are dead, I doubt choosing sexual reproduction will be logical(won't have active body fuction to produce sperm). So, asexual methods like splitting, budding or some methods that plants use, may work. You know what, fuck logic, you're gonna have dead men talking, so use any method you like or find interesting for plot
You are grossly underestimating human efficiency if you think we'd just try to kill them.
Waste of very durable workforce
Also, aren't you already assuming genetic reproduction if you go with evolution?
Hmm? I thought by killing humans he turned all of em' into zombies