Great thread. I have always loved the science fiction based on possibilities of alternative space travel.
The one that I thought the second cleverest, maybe more practical than the elevator, was an orbiting reverse rail-gun. A large tube, in low earth orbit, filled with the machinery for electro-magnetically catching and accelerating a vertically-launched spacecraft that shows up at just the right time and place to go in the mouth of the tube. (If you miss just a little it is messy ) A big part of the problem, (like with the elevator) is to get enough stuff in orbit to build the "catcher". Probably possible make it mostly self sustaining, with solar power collectors, and using that power to run an ion engine (maybe use the left-over fuel from the caught launch vehicles as reaction mass?).
But the best idea, was the "launch loop" described here. To get above the atmosphere. Just from size, a combination of the orbiting rail gun with a launch loop is going to be much cheaper than the elevator (we are talking ~40,000 miles long for the elevator?). All of them are pretty vulnerable to terrorism though.
Frank, my math is a little too rusty to be sure, but I think that Sri Lanka is a little too far from the equator to be stable as an attachment point for a "bean stalk". Just thinking about it, I suspect that the top of the stalk will have a daily drift, back and forth, from directly over the base, to a point equidistant from the equator on the south side. But a nice picture. I took the liberty of rescaling your KML a little to make it a little more "realistic"?
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) A big part of the problem, (like with the elevator) is to get enough stuff in orbit to build the "catcher". Probably possible make it mostly self sustaining, with solar power collectors, and using that power to run an ion engine (maybe use the left-over fuel from the caught launch vehicles as reaction mass?). 
