Note your launch cost analysis is not useful: the entire ribbon doesn't need to be put into space. The best and cheapest way to build the elevator is with a seed string.
My launch cost numbers were to LEO - GEO is a lot more expensive - and so was only ever intended as a ballpark figure. The seed string itself needs to be lifted and I'd be very surprised if you could do that for under a billion. Sufficient strength of carbon nanotubes to be self supporting (based on theoretical models - we still can't actually build them) would come in above that for launch costs.