It's a ring, so it should be thought of as something pi1000km in length, not pi(500km)^2 in area. The inside of the ring is not used for the structure. $32,000/meter sounds pretty generous.
That's a good reference point. Cost for infrastructure projects usually isn't linear. I've seen an exponent of .6 used to extrapolate costs.
(3140km/27km)^.6 * $4.75B = $82B. Adjusting for inflation gives you something a bit over the $100B. They probably came up with the number in a similar fashion.
Do you know if your number includes the detectors? They would have contributed significantly to the total cost.
Which is around $175,900 per meter.