Let's leave speculation about the design for another discussion, and consider the logistics of recovering it after its mission.
The Falcon 9 second stage can get to orbit. Now, suppose you could get it back in good shape. The location for splashdown would most likely have to be a long way from any land mass. Presumably, it would splash down in the Pacific.
The great distances would cause a delay. If you want a fast turnaround, this is a problem. How to overcome the vast distance back to Florida?
Idea: Put a rocket inside one of these planes. Why? To speed up processing. It may need to splash down in the Pacific, be transported by boat which docks at the nearest island with a suitable airport. The rocket is loaded in the plane and sent back to Florida and unloaded and processed for the next launch.
Boeing 747 Large Cargo
Aero Spacelines Super Guppy
Aero Spacelines Pregnant Guppy
It says on the link that the Pregnant Guppy actually transported the Saturn second stage rocket. The S-IV second stage dimensions were 40 feet long by 18 feet in diameter. The last stage of this rocket, which was never flown, was the Centaur. But the Centaur stage was the Earth Departure Stage. The second stage, presumably, could get you to orbit. (cross your fingers, there)
You might need to work on the size of the rocket, but since this kind of thing has been done before, it isn't out of the question.
This is actually an interesting subject. I've been reading about it this morning. It so happens that the Ares I second stage has a design very similar to the Saturn second stage mentioned. However, it is an expendable design.
Secondly, the cost of an Ares I is high, but can come down if there were more launches. The cost of launches can be brought down to a comparable cost of the Soyuz, which we are renting from the Russians. If you were to make the Ares fully reusable, frequent launches would be desirable.
Instead of a capsule on top, try putting a Dream Chaser on top. It may look something like this:
|Dream Chaser on top of an Atlas|
There is surplus cargo capacity, so that there is more mass capacity for extra hardware in order to make this happen.
The first launches could use expendable second stage. Development can continue so as to make it fully reusable and then you can proceed to make the turnaround go faster.