Regarding the GDP needed once you have a working "mine from the moon and send to orbit" economy it doesn't seem to be too bad. The assumption would be that a lot of technology is already developed for other projects. Launching it all from earth obviously wouldn't be possible even with vastly cheaper launch. That's why they put the build into the moon-earth L1 lagrange point to be easily reachable from the moon.
For propulsion and reactors, but there are multiple projects today working on all of this. Building a life support system for 400 years is still an unsolved problem however.
Re: spin. I still claim that the best design is to rotate entire living module as one. Most of the activity is going to be on the outer shell. Warehouses, etc will be in the lower gravity inside. No moving parts.
The only question is what to do with fuel and retro engines. Rotate them as well? Fuel tanks need to be stronger. Do not rotate? Then maybe living module can undock for the flight and rotate separately.
These are supposed to be generational ships. Now imagine you need to take the primary drive down for maintenance? What does the moving colony have for power?
I'd want tri-redundant systems at a least, for everything.
My washing mashine self destructed a few times. I don't want to put my children inside one for 400 years.
I'm sure every parent has thought the opposite at least once.
I guess they were replaced a few times during the non harvesting season.
To replace the main gears of a rotating shell in space, you must "turn off" gravity for a week (or month).
Power provided by toroidal nuclear fusion reactors in the outer shell of the living module, but why do you need such reactors if your primary propulsion is provided by Helium 3 - Deuterium Direct Fusion Drive? If you have direct fusion technology, you don't need toroidal reactors.
Rotating inner shells mechanically for 400 years is terrible design, it's much easier just to rotate entire structure. Once it's going it keeps rotating inertially!
Another comment points to error in speed calculation - at declared acceleration they should go at 0.1c, not 0.01c!
And what is missing of course is the calculation of how many years of current world's GDP is required to complete such project event if all yet-to-be invented technologies exist.