You have three options. The first would be to motio track something like the top of the building that is closest to the moon then apply that tracking info to a null and a parent the moon to the null. If the top of the building goes out of frame you can just stop tracking then pick up the track when the building comes back into frame. You then have to set a couple of keyframes by hand to make the shot work.
You may also be able to camera track that shot and then set a ground plane and origin and a reference null. You would then make the moon layer 3-D, hold down the shift key while parenting the moon to the null so the moon layer snaps to the null's position, then adding some extra Z space to the moon and scaling it to fit.
If the camera motion is fairly smooth easiest option may be to set up some kind of guide layer so you know how far the moon is supposed to be above the building at the start and end of the shot and then keyframes frames for position for start and end. You then move to the apex of the camera move and set another key frame for position for the moon. You can then open the graph editor and adjust the speed curves to make the shot look right. This last option may be the simplest. It's hard to say.
I just thought of one more option that would work perfectly if you have something in the shot that stays in the frame. You could stabilize motion usingthat point then position your moon, then add a null and tie the nulls position property to the anchor point of the footage, then parent both the footage and the moon to the null to remove the stabilization and add the camera movement to the moon.
Excellent! Thank you so much. I'm experimenting now with the best of those options for this particular scenario, as I'm now dealing with putting in a better version of the fake sky in there and masking it up with the horizon line. I did a quick test run of option 3, and it works pretty well - just gotta smooth a few sections where the moon dances a bit.
Again, thank you for your help!