It may be true that the Moon's annual path isn't precisely periodic, and isn't precisely a closed curve, and that its center of survature isn't precisely in the Sun-Earth-Moon plane.  But it's close enough.  So let's not get distracted by things that aren't important to the broader discussion.

I acknowledge, again, that the Godfray and Turner references say the Moon's annual path is concave.  But there are other references that describe it as convex.  I see no reason to believe that the Godfray and Turner references are any more reliable on this point than the other references.

Terry0051, I'm going to ask you the same questions that I asked Marc Kupper about what your source is for the distinction between convex/concave when looking outward from the inside, and convex/concave when looking inward at the entire system.  But before I ask you all those questions, I'll let Marc respond to the questions I asked him, since he might resolve some of them. -