I came across your project perhaps too late to suggest drafting a space elevator based on a completely different technology.
The original reason for my recommendation is because it seems that a rotating tether does not have much in common with a skyscraper as is the name of this forum (SkyscraperPage)
What I am recommending goes by the name of a SpaceShaft and it could truly be regarded as a skyscraper instead of a centrifugally rotating tether.
You can find some information about it by searching the internet for the word spaceshaft, (yes all in one word,) but if you care for a quick explanation on how such a structure would work or be deployed you can read more below.
Imagine a spar-buoy with a line at one end that extends to a submerged anchor. In water, such a buoy will have half of its body submerged below a waterline while the other half will be floating upright above the water. If, metaphorically speaking, we assume an environment in which the atmosphere of our planet is the equivalent to a water-mass, while the Space is the counterpart of the atmosphere, then if new buoyant sections could be inserted at the base of the buoy, where the anchor-line extends to the underwater anchor, and if by some mechanism, slack could be given to the anchor-line as needed, then the top section will rise further into Space.
Evidently such a structure will have to have, besides the anchoring system, some mooring system to keep it from being tossed around by winds, but it will produce a tremendous amount of up-thrust making it besides a skyscraper a combined method of construction and transportation.
As said, perhaps you can develop some ideas about it which will make you the very first to conceive some artwork related to the concept. If you are interested go to
http://spaceshaft.org
Cheers