Occupying a Ringworld and controlling it and its defenses are two different things. As mentioned, it would take 1000+ years to figure the place out if your completely dedicated to the initiative. At that tech level it is doubtful that TL15 Imperium and the others are going to figure anything out quickly.
It might take that long for the Imperium to figure out how to make their very own stellar gas-dynamic laser.
I do not think it will take the Imperium 1000+ years to translate the control panel and figure out which is the "Fire" button.
Also, the calculations on land mass vs the Imperium are probably off. We really only have a good picture of Imperium mainworlds and only rare glimpses at other system worlds.
According to canon, the Third Imperium had 11,000 star systems, with an average of one inhabited planet per system.
http://wiki.travellerrpg.com/Fourth_Imperium
If that was off by a factor of ten, it would have 110,000 worlds.
Which would mean the Ringworld would only have room to hold about 27 entire Imperiums.
If you cut the ringworld and laid it out flat, it would be 1.6 million kilometers wide and 960 million kilometers long.
Which means you could place about 123 planets the size of Earth side by side within the width of the Ringworld, and about 74,000 Earth sized planets within the length.