So the one hard number you offered is that we are "100,000 times better at moving material around in space than we are now."
I'm going to give all the benefit of the doubt to the numbers that make your case the best. Let's use the cost it currently takes to put a kg of matter on the moon. Current costs are around 1-1.2 million per kg landed on the surface. But let's be generous and say that with the next generation of reusable rockets we can reduce that to 100,000 per kg. That's nice, because if we assume we get 100,000 times better, we can use the nice even number that one day we can move mass to the moon for $1/kg. I'm assuming that the 100,000 times number includes getting the mass from somewhere other than Earth.
The moon has a radius of roughly 1737 km. Therefore, the surface area is roughly 3.79×1013 square meters.
On Earth, a column of air that provides sea level pressure is about 1.03kg per square centimetre, or roughly 10,000 kg per square meter. On the Earth, because of 1/6 G we would need six times the mass. But let's assume we can get by with half the pressure., so we only need 3 times as much. So, it will cost us about 30,000 per square meter of the moon's surface, or 11.1 X 10^18 dollars.
The annual GDP of the Earth is 80.68 X 10^9 dollars. Dividing the two, and you find that it would take about 137.5 million times the Earth's annual GDP to pay for it.
Dropping comets on a body is the standard proposed way to terraform it. This would not work for the Moon, because any comets of a size big enough to matter impacting it would throw a whole lot of debris at the Earth. Bombarding the Moon with the thousands of comets required would likely devastate the Earth. Also, when a comet hits an airless world, the impact will vaporize it, and a lot of that vapor will be lost to space. That's a serious problem, but we'll skip if for now to make things look the best for your scenario.
Then you have the problem that the Moon's soil is full of unoxidized iron which would bind with oxygen in the atmosphere, that the moon is also depleted in necessary chemicals like carbon and nitrogen, and the long lunar days and nights would likely play havoc with your new atmosphere.
There is a much better solution. There are likely hundreds to thousands of 'lava tubes' on the moon, and some are so large that you could put entire cities in them. For example, the Marius Hills lava tube has been partially radar mapped and is at least 50 km long, 70m deep, and 500m to 1km wide. Even pressurizing this would be a monumental task, but at least it's in the realm of feasibility in your future world.
Purdue university has calculated that a stable lava tube on the moon could be as wide as 5 km with a ceiling 1.5 km high. Some lava tubes could be hundreds of kilometers long. That's thousands of cubic kilometers of living space. In one lava tube.
The GRAIL mission discovered that the moon's crust is about 12% void space. A lot of that is small, but there is bound to be more living space underground than we would need for a very, very long time.