There is a fatal flaw in the proposal. The strength of the outer skin needs to obey the hoop stress equation. The tension in the external member equals internal pressure times the radius. For 6.5 km diameter and 15 psi inside, the skin strength must be 20,000,000 pounds per linear inch. If made of high strength steel (77,000 psi) the skin must be 20 feet thick. Windows of fused quartz would need to be 228 feet thick. Much smaller cylinders are required, no more than about 200 meters in diameter.
These designs weren't drawn up by the stupid, Bill. They were done by physicists, astrophysicists, and engineering experts in their fields. They've worked on the ideas and plans, and potential problems, for that particular physical environment, so different from our environment, for fifty years now!
As I, myself, have said many times in the past decades, I'm not a fan of any "Islanded Space Ark" city-state colony other than a Stanford Torus spin-gravitied inner tube inside a massive integrated protective outer-tube that does not spin. But an O'Neill double-opposed cylindered Island-3 colony is possible. Megastructures that would be impossible to even think of on Earth are very possible in the physics of the outer-space environment. The amount of mass material thicknesses of the colony shell masses you contemplate and mention as necessary will be no problem whatsoever regarding these colonies, every O'Neill Island-3 double cylinder will have a total shell material mass of a small asteroid, not only for wanted integrity but for wanted protections against much of the unfriendly environment of outer-space.
There will be no immediacy regarding O'Neill Island #3s. It will be tooled up to -- worked up to -- via smaller islanded custom station and colony structures. Though I don't favor it, as I say, I press that when that size is reached, there be no larger structures ever as totally unnecessary. Many should be favored over an increasingly 'Titanic' quality lump. By that time we should be reaching out into the universe looking for many new mainframe worlds like the Earth and Mars . . . who needs a stone coffin-tomb of 'Dyson's Sphere'?