Being a HAM myself I have known of EME contacts for many years.
It's not the power of the amplifier, it's the gain of the antenna.
If you look at the link below you will see the wattages used by several people for EME transmissions. One of them is a mere 35 watts. You are not going to disturb the neighbors with that low of power.

http://web.telia.com/~u87120967/emegallery.htm

It's definitely possible in my book.