In fact, he is sure that it isn't be caused by an outside perturber.
"In principle, a viable
candidate would be a putative trans-Plutonian massive
object (PlanetX/Nemesis/Tyche), recently revamped to accommodate
certain features of the architecture of the Kuiper
belt and of the distribution of the comets in the Oort cloud,
since it would cause a non-vanishing long-term variation of
the eccentricity. Actually, the values for its mass and distance
needed to explain the empirically determined increase
of the lunar eccentricity would be highly unrealistic and in
contrast with the most recent viable theoretical scenarios for
the existence of such a body. For example, a terrestrial-sized
body should be located at just 30 au, while an object with
the mass of Jupiter should be at 200 au."
This is in stark and direct contradiction to research he himself did to determine the minimum distance to any hypothetical massive body.
[link to arxiv.org]
"We obtain the following approximate lower bounds on dX for the assumed masses of X quoted in brackets: 150 - 200 au (m_Mars), 250 - 450 au (0.7 m_Earth), 3500 - 4500 au (4 m_Jup). "
Furthermore, the anomaly he was studying is orders of magnitude too small to be seen by telescope, let alone by eye (it was only found using decades of extremely precise lunar laser ranging), so no you and your friends are not seeing anything wrong with the moon.

That's because you're ignorant of how the moon should look and move.
Thread: Live video of the moon showing field rotation and the moon's exact position in the sky! 10-2-11 Summary on page 4!! (Page 4)