There you have it.Just to clear this up, it is a modern, 20th Century space shuttle. Apparently the clue about landing at Kennedy Space Center didn't make it clear enough for some people. I chose the modern space shuttle so that the project did not involve constructing an item directly associated with any particular SF series; the technology should be easily within the grasp of any space-faring race.
I state again that the exocomps do not entirely need designs and schematics of the tool that which they want to replicate. To be sentient is to have self-will, and they could use that self-will to think up a tool for the job. Not to mention, they may have god knows how many tools in their data storage. Again, the astromechs are good, no doubt, but their limited tools will be a burden. Not to mention, that some of them would be absolutely useless toward the construction of a space shuttle, such as the little thing that shot the lightsaber out, or the buzz thing (shooting Ewoks, not the buzzsaw).