For example, if we took the vehicle (since it doesn't have to be the space shuttle as per the OP) up in your space elevator and dropped it from some height that would count as "space", then would we be able to slow it down enough to have a "cool" re-entry?
I think that it does sound possible.
Maybe. Depending on the height there might not be enough atmosphere for parachutes to be effective.
(Too great even assuming the 0 speed relative to the ground when starting?)
0 velocity relative to the ground does not mean 0 velocity relative to the surrounding atmosphere. In GEO you're still moving through the atmosphere at over 3km/s.
I think that it does sound possible.
After the massive horizontal velocity relative to the ground is taken care of somehow, then I think it would be reasonable to assume we could build something that would allow for cool re-entry.
Am I way off?
You couldn't. As soon as you start reducing the "massive" horizontal velocity relative to the ground you start falling. You could theoretically modulate your height by modulating your horizontal velocity, but you get to a point where to make your re-entry smooth you're travelling too fast to make the concept very useful.
Here's another idea, some mechanism to absorb the heat, run a stirling engine, which runs a nitrogen compressor, which has coils to cool the surface. The heat from the compressor and condenser would be thrown behind the shuttle, keeping the front portion cool. Basically you're using the heat to combat the heat. In the end it creates more heat, but at least you can put it where you want (behind the shuttle). Sounds too simple though, probably would not work.
Why bother? All you need for the front to handle the heat of reentry is a layer of ceramic tiles. It requires little maintenance, no active energy consumption, and there's less that can go wrong.
Would a heatpipe be more efficient?
If you use energy to speed up energy transfer, then you can get massive thermal gradients that can't be achieved with passive heat transfer, and you can also modulate the rate of thermal transfer depending on need. But again, heatpipes would be more simple, cheaper, and wouldn't go wrong as often.