[dabluecaboose]

>There must exist a lunasynchronous orbit that would remain over the earth side of the moon, though I'm not sure if its close enough to the moon to avoid being perturbed by the earth and kicked out.

Selenostationary orbits (The astrodynamics terms generally take the Greek name) are indeed unstable and vulnerable to perturbation. Instead, you can have a trajectory around one of the Earth-Moon LaGrange points (points where the gravitational pull from each body is equal)