I'll throw something into the fray, not as a "dub," but just as an observation.
I haven't studied anything on the subject, so these comments are not derived from any great personal knowledge:
Man has only been studying the moon to the 'inch' degree for a relative short time.
Is it possible that there is a movement cycle that spans a greater time period than the observational period?
For example, if I looked at my neighbor for a minute, I might observe him moving away from me. A longer observation might reveal that his direction away from me was not sustained.
Is it possible that earth's gravity has long term cycles of fluctuation that affect the distance of the moon?
Is it possible that there are fluctuations in the theoretical 'Higgs' field that are beyond our observation for now?
Concerning the Higgs Effect see here.
Is it possible that long term fluctuations in the Sun or earth's orbit around the Sun have an effect on the distance between moon and earth?
Is it possible that there are fluctuations in the theorized 'dark matter' that have an effect on the orbital distance of the moon?
Concerning 'dark matter' see here.
I agree with your point that the distance of the moon to the earth can have beneficial and/or catastrophic consequences.
(In the remake of "The Time Machine," the breakup of the moon is shown as causing the demise of modern society. (See here)
But I tend not to put a lot of faith in long-term conclusions drawn from relatively short-term observations.
Also, if God does exist, he is a factor/force that has been left out of the conclusion. This would necessarily throw the conclusion into question the same as any hypothetical conclusion of my stepping off a roof top would be in error if I did not take gravity into account.
You said that "originally the moon was extremely close." I thought that the theory held by most was that originally the moon was part of the earth. Of course, that might be what you meant by "extremely close." It could be that I haven't kept up with the latest ideas. But that leads to another question:
Is it possible that the moon's distance is still settling out from its original movement away from the planet. If this was the case, then, it might take a longer observational period to confirm. Also the (admittedly theorized) settling out speed might be affected by other factors as I mentioned above.
I imagine that most Witnesses (or other people of faith) would express the idea that God would take care of it, one way or another, just as He would take care of any possible burn out of the sun or any other possible astronomical problem that was beyond mankind's control.
For example, compare Psalm 115:16.
Take Care