This is not a real answer, but it seems that in more than 3+1 dimensions we can't expect stable orbits. And the "inverse square" law for n dimensions is 1/r^(n-1). Which, for 3 dimensions plus time, give us 1/r^2.
What does that have to do with lunar orbits? Generally the 1/r^2 law is valid when the size of the source is small compared with the distance to the source. That is to say, the 1/r^2 law is always rigorously correct, but the interpretation of r might not be what you think it is when you're close to the source. That is true for gravity, for the exposure from a source of radioactive material (that's closer to my job), quite generally, and it's geometry, not specific to the properties of a radiating or gravitational source. If the moon has a non-spherical mass distribution, then it will have multipole moments, which means 1/r^4, 1/r^6, and so on. Which are not 1/r^2. That is, not stable. (I can't recall off-hand if odd moments are a thing.)
And, for reference, the diameter of the earth is about 8,000 miles, while an orbit could be around 100 miles. Or 200, or 400. At any rate, the distance of an orbit from the surface can be much smaller than the diameter of the body -- it's common for orbits to be not much larger than the size of the body. Which means you can't just assume a point source, you need to know something about the multipole moments, that is, the mass distribution.
So anything that deviates from 1/r^2 can't be considered stable. So lunar orbits are only stable if you are far enough away. The moon has a non-spherical mass distribution, so if you're close compared to the diameter of the moon, the orbit can't be stable.
I still haven't demonstrated to myself that angular momentum is transferred. It seems likely, since a non-spherical distribution gives the satellite something to grab on to, so to speak. But I haven't run simulations or anything to demonstrate it. So this is an incomplete answer. But it would seem you don't even need to show that in order to know that orbits aren't stable for 1/r^(n-1) where n>3.
Higher Dimensional Gravity