With reference to Indy's "space shuttle" comment.....
>>The question is which arbitrary claim most closely matches reality.>>
If you liken it to an internal combustion engine, then of course your view more closely matches up to THAT. But it is nothing at all like that. Let me ask this...when the returning space shuttle first begins to hit the thinnest part of the atmosphere, and travels for (say) 100 horizontal miles, how much of its speed is lost to friction? NOT MUCH. And it would be even LESS if there were a train of 1000 shuttles right behind one another. The last one would lose very little of its energy to the atmosphere.
The comparison is not to an internal combustion engine, but to a steam engine. The steam could be provided by internal combustion, nuclear power, geothermal heat, or tidal flexing. Steam processes are typically much less than 50% efficient at delivering their energy to the end result. There is no reason to think Brown's process will be any better.
Not all of the material is going to be in the "thinnest part of the atmosphere." There is a lot of it that's going to be along the boundary layer between the rising column and the atmosphere.
I'm not sure what you mean by your Shuttle analogy other than a stream of material near the center of the rising column will have no interaction with the atmosphere on its way up. I think that's pretty much a given.