That's what you believe because you are incapable of thinking outside the box.
I notice you use that a lot as an almost proxy argument. I favor thinking outside of the box, but just because you are outside the box does not mean your argument is sound.
There have been many good points raised against this idea and you have ignored most of them.
But I want to narrow on just one. The whole asteroid/meteor thing is not an advantage to your moon ship, but rather a huge draw back. Such a massive object as a moon would be more likely to be hit, with little to no hope of dodging, and may even attract objects. A head on collision with your accelerating moon ship would be devastating. Structures built on the inside, or carved out would collapse. People would simply be buried alive. If you want to say that the interior would be built in such a way as to withstand this, than you have negated the need for a moon. The construction necessary to build such an interior would be better served to simply build a ship with a lot less dead weight. If you want to use a moon, simply harvest it for the resources to build the ship, or better yet use an asteroid or two.
A smaller ship would be much less likely to hit or attract such an object, and actually stand a chance at dodging in the event it needs to.
This much has been pointed out already, but I bring it up because even if we can set aside all we know of physics and accept that this moon project has a chance, you still have to tell us what you plan to do to avoid this problem.