To me a heat exchanger is something which moves heat from one medium to the other, and is not necessarily part of power production. The radiator in a car is a heat exchanger, and not a power generator. Thus, I did not understand your viewpoint.
Quoting from the first link you gave: "Pumped through a heat exchanger, that hot lead will help generate steam just like a conventional thermal power plant". Thus, I consider it as not a power plant, because it only produces steam. While I see that you consider the production of steam to be sufficient, likely because it reduces the issue to a previously solved problem.
I am satisfied that the General Fusion design, which hasn't even started, is not a nuclear fusion power plant of the sort that Asimov predicted would be available by 2014. That is my primary interest in this discussion.
FWIW, after more looking around, I found this quote from http://www.technologyreview.com/news/414559/a-new-approach-t... :
> However, if the company can pull off its test reactor, it hopes to attract enough attention to easily raise the $500 million for a demonstration power plant.
Note how that magazine author also distinguishes between "test reactor" and "demonstration power plant"?
The information I found are not sufficient to make the estimates that you mentioned. For example, while I found pictures of the small sphere experimental setup, and a mention that the final velocity is 50 m/s, I did not find learn the mass of the piston, or equivalently the amount of power used to drive it. Nor did I find out how much power goes into the plasma injectors. There are images of some pretty hefty capacitor banks, but I couldn't tell if they are discharged at once, or if they are rotated through in order to lengthen the charge time for any one bank of capacitors.
Estimating the pumping needs is very complicated. I found no reference of what the internal surface of the sphere looks like. If liquid extends into each piston then there well be turbulence at each interface, causing power loss. Even if it's laminar, I still need to know the rotational speed.
The depictions I've seen show that the lead surface is a near cylinder, which means a very high speed, as the natural shape of a rotating fluid is a parabola. Assuming 0.25 meter radius for the upper part of the cylinder and a height of 3 meters gives 400-500 Hz. That seems rather a lot, given that they're talking about some 50 cubic meters of lead, or 500 tons, moving at some 2,000 m/s.
(I used the equation for a liquid mirror telescope: h = 1/(2g) * (omega * r) ^ 2. Hopefully I didn't calculate it incorrectly.)
Since the information I've found doesn't make sense, either my math is wrong, or the information I've found is incomplete. Since you are the one who believes that this is a near-term power plant, then surely you must have worked out these details already, or read them some place. That is, how fast is the molten lead mixture supposed to rotate, and how much energy is needed to keep it at that speed?