That was in Middle Ages
Medieval Civilization (at least in Western Europe) is based on a mixture of both Germanic and Roman traditions. It is an entire copy of the old Roman traditions. That was in the Middle Ages, yeah, but so far no country has surpassed them or reached concerning most measures of human progress, except maybe for some East Asian nations, which applied many concepts from Europe. Why merely create a great idea (like Ancient Greece did) if you don't apply it in the end?
The folks that were "invited" to bring know how and so on were craftsmen, clergy, traders and so on
If only those were invited to settle Eastern Europe, then there wouldn't be entire cities and villages populated by Germans. They were not there only for trades. They were also called for defense against invaders and they did bring agricultural techniques to those lands. One needed many people back then.
They aren't really "Germanized", they are "westernized" If anything.
I prefered the word "Germanized" because not only is it the implied form in some works on culture, but also channel through which Westernization reached them. "West" is too broad, as it includes many cultures like those of Celtic tribes and Latins, not to mention the cradle of Western Civilization, Greece, none of which are too similar to Germanic folks, despite some commonalities. But let's not mind the wording as long as we can get our message across.
You seem to be too much into stereotypes and some kind of biological/cultural "racism".
This is not a post concerned about race. Anyone at any given moment can wake up and say "hey, I will start to do things better from now on". It is a matter of culture, upbringing, history.
Of course having money helps in that it provides a facade of good manners when behind it all there is a corrupt society. Many examples of such instances. One should place a bet on not the current situation of a nation, but on the cultural profile of that nation to know if it will eventually yield results. Since the times when most nations of earth were level in GDP per capita (PPP), many would praise Germans and other such peoples for their many qualities. Such things as hygiene, modes, education, values are strongly cultural.
The center x periphery theory is known, sure, but it doesn't explain the many exceptions. Finland neighbors Russia, for example, but they don't seem to have taken much of each other. Also, if we have a "center" and a "periphery", don't think those in the center were doing something right, as you yourself said, for thousands of years, to become a center? One doesn't become (steadily) rich out of nowhere. It is a longterm thing (unless of course you discover in your land there is something very precious and then you start making money out of that, instead of having to invest in a better population).
Otherwise you would have to conclude that people from Dubai are "culturally superior" to people from Argentina, China, Canada or even... your beloved Germanics :)))
Canada is a British and French creation. Argentina and Chile are not by far more successful than the rest of Latin America. If anything, they are faring as great as Croatia, especially Argentina. In fact, back in the 20s Argentina used to be one of the best countries on Earth. Theirs is a history of constant decay due to corruption and mismanagement, not attaining the same stats as now the likes of Australia, Canada and the US do. Chile might be doing better now, but should I mention that many Spaniards who settled in Chile are of Basque descent?
Miguel de Unamuno once said: "There are at least two things that clearly can be attributed to the Basques: the Society of Jesus and the Republic of Chile."
That's correct of course but how could it be different If you include the history of those lands ?
Ok, including the history of those lands, how does that change the reasoning? The Mongol Invasion is the end-all-be-all why they lag behind Western Europe now?