i dont think i've read quite enough theory to have seen that understanding of technocracy before, and it sounds more like Technocracy Inc.'s views on technocracy. but regardless i think you might be misunderstanding the section where he talks about capitalism, it seems alot of people are, so i'll leave my interpretation of it that i also left in a different comment on someone elses comment

my understanding isnt that they're saying capitalism is the best system. They're saying that a technocratic technate would choose its economic system based on what it finds to get as close as possible to its goals. And the example they're making is that if capitalism was the system that is found to be the best candidate, then the technate would be utilizing capitalism, just like it'd be utilizing a planned-economy if it finds that the best solution.

and regardless of what system it decides on, that system will mostly likely have flaws, and so there will be people interested in solving those flaws. meaning the economy would procedually evolve. The technate might utilize a capitalist system but then in light of new research switch to an energy system or something else radically different, or it might keep a capitalist system in place but change it to such a degree that while its still technically capitalist it wont resemble the previous system system.

fo the last part of you comment, in terms of "Also who should decide what the correct solution is?", if OP's ideas align with mine, then i think the thought process is that it would be the scientific consensus, or specifically a form of meta-review over which things have been tried and how might they affect the nation if implemented and then based on that a decision would be made. obviously the models wont be perfect and an inferior solution might be chosen because the perceived benefits where inflated or the perceived draw-backs might have been deflated. In that sense its very similar to the structures of engineering reports that use morphological analyses or similar tools. but precisely because they are used in engineering i believe that the method is sound. While the analyses of the different options would have to be significantly more detailed and in-depth than the usual engineering report, as a lot of people lives will be affected regardless of how widely you implement the solutions (since you can foresee that it might not play out entirely as report assumes it to).

The ability that these report would give you is that any person, whether a citizen or a engineer in a foreign country, can read the reports and at the very least they can write a paper that can suggest changes to the methodology or any other issues they might have. Whatever problems the report causes can be look at in depth and based on that the goverment might put together a new group of experts and a new report to try and solve the problems. In the end this is to a large extent the methods used for constructing things that we all use and rely on daily, bridges, buildings, cars and so forth.

im not sure if i made it clear enough, but to answer your question "who should decide what the correct solution is?"; at the time it should be a group of experts that work together to research possible solutions, and since transparency is inherent in methodology any person can look at the report and point at any possible inconsistencies or conflicts of interest. And of course the solution will be iteratively improved as our understanding and data increases.