There's a section on building bicycles in the middle ages in "a Connecticut Yankee in King Arthur's Court" which plays a similar thought experiment and which you might enjoy.
But to answer this question seriously: there is a form of Moore's law that has been in place at least since the late middle ages, and probably for longer, coming from the fact that any economic model that takes into account both goods and capital (the machines and infrastructure to build more and better goods) has a compounding growth component. This is true even if you ignore cultural and scientific advances and only look at physical capital.
The first steel was ridiculously costly to make, and a commoner's life savings would buy in the ballpark of a kilogram. https://acoup.blog/2020/11/06/collections-iron-how-did-they-make-it-addendum-crucible-steel-and-cast-iron/. But to produce steel more cheaply you need several tons of "manually" created steel to build a bessemer converter. The components for this giant industrial machine have to either be built by hand (again very expensive) or be precisely machined in factories, in machines. Those machines are built out of precisely put together steel (or less reliable iron) components, which need either simpler factories or ridiculously costly manual processes to make. And so on.
A simplistic but successful way to model this is to assume that the cost of creating new capital (factories, plows, etc.) has a dependence on existing capital. This results in compounding growth. If you ignore things like population growth and accumulation of knowledge, the growth will not quite be exponential, but definitely very non-linear.
Not only is setting this up expensive, it needs to be set up in a society where most of the population is subsistence farming, so there is very little surplus to put into building better capital, meaning that take-off would be slow. Furthermore, in addition to building up the industrial production line you would have to re-build the supply chain, since many industrial materials are geographically isolated and need to be imported.
So even if you somehow guaranteed that everyone in a middle-age society had a modern education and had a Wikipedia-level level of knowledge about the modern production line, guaranteed open trade routes, eliminated wars, etc., my guess is that it would still take multiple generations to get to modern technological levels (though certainly having modern knowledge and cultural institutions would speed things up by a lot). I seem to remember reading about an estimate of this somewhere (in the contexts of how long it would take survivors to rebuild after an apocalyptic collapse of society). I don't remember where this was and the answer they came up with, but my very un-informed range of guesses would be something between 3-10 generations assuming optimal conditions.
My impression of the proposed idea is to create a "hard" intellectual accountability system for intellectuals by sampling some "falsifiable" subspace of idea space, similar to what exists for superpredictors and athletes. This certainly seems helpful in some areas, and I think is similar to the purpose of politifact.
But then there's the risk of falling into the Marxist mistake: that if something isn't quantifiable or "hard" it is not useful. The idea that "hard" production matters (farmers, factory workers, etc.) while "soft" production (merchants, market researchers, entertainers) does not, which is at the base of Marxism, has been disgraced by modern economics. But this is kind of hard to explain, and Marxism seemed "obviously correct" to the proto-rationalists of the early 20th century.
The sphere of intellectual expertise, especially the even "softer" side of people who've taken it on themselves to digest ideas for the public, is much harder still to get right than economics. No matter how many parameters an analysis like this tries to take into account, it is likely to miss something important. While I like the idea of using something like this on the margin, to boost lower-status people who get an unusually high number of things right or flag people who are obviously full of it, I think it would be a bad idea to use something like this to replace existing systems.
The official guideline is 60C for 30 minutes. https://www.hindawi.com/journals/av/2011/734690/ claims 56C for 15 minutes is enough. Personally, for homogenous wet stuff I would heat until close to boiling/fizzing, then wait 5 minutes and feel safe consuming.
Advice: when prepared food contamination risk becomes high, order in food that can be heated and microwave it thoroughly before eating