Let's do a bit of math.
According to Wikipedia, the mass of the moon is $7.3\cdot10^{22}\,\rm kg$ and its average orbital speed is $1.0\,\rm km/s$. That means its kinetic energy is $3.7\cdot 10^{28}\,\rm J$. According to the virial theorem the potential energy is $-2$ times the kinetic energy. To get the moon away of the earth (that is at potential energy $0$), you therefore need to add at least the same amount of energy as the moon's kinetic energy again.
So we are looking at a method to add $3.7\cdot 10^{28}\,\rm J$ to the moon. For comparison, the largest nuclear bomb, the Tsar Bomba, releases an energy of up to about $240\,\mathrm{PJ} = 2.4\cdot 10^{17} J$. That is, you would have to detonate about $1.5\cdot 10^{11}$ Tsar Bombas to get the energy; that's 150 billion bombs. Even at the height of the cold war, there had "only" been 68 000 nuclear weapons. So you are looking at an arsenal two million times the total arsenal of the cold war. And that's assuming you manage to transfer 100% of the energy the bombs release to the moon, which itself is rather unrealistic.
Another bit of trivia: A year has about 30 million seconds, therefore 500 years have about 15 billion seconds. So you'd have to build ten Tsar Bombas per second.
Or in short: Forget moving the moon. Better think of ways to kill the wasp.