I feel like this is risky. Our MC decided to raise the villain's popularity so that when she falls, she'll have more to lose, but it's a bit much to gamble on the villain deciding to sleep with the guy a second time. Yes, Tang Meiji will sleep with the guy again, but that's because the mangaka decides how to plot goes.
It feels like the MC is making random guesses and the mangaka is making the villain do what is guessed so that the MC looks intelligent and cool. But if this had been a real scenario, then the 'hot search' scare would have made Tang Meiji momentarily frightened enough to not sleep with the guy again in the future and aim for someone without a wife and kids, thus ruining our MC's plan.