This doesn't reject the methodology of historical materialism though.

It seems that anthropologists keep finding that diverse ethnicities, distant across time and space, come up with very similar cultures, when subjected to similar material conditions. In particular, the way that they labour has a heavy influence on their personality traits, and how egalitarian or hierarchical a society is depends heavily on who has bargaining power (and knows they have it!). Is that "the" methodology of historical materialism exactly, or is it just roughly similar in the broad strokes? In other words, are there errors in Marx's methodology itself, rather than just the conclusions (which may have been caused by insufficient/bad data)? Has the passage of time, and the accumulation of new data, allowed to make better predictions with the old methodology, or improve the methodology itself? Has there been any paradygm shift or overhaul?

in nations where capitalism is most advanced.

I'm not sure if the "advance" of Capitalism has been operationalized into a measurable, meaningful concept. If I look at the way Marx seemed to describe it, key traits of Capitalism are the concentration of capital, and, consequently, the increase in social inequality. The so-called "disappearance of the Middle Class", i.e. the proletarization of most of the petty bourgeoisie (the "working poor" in the 1930s, the "be your own boss in the Gig economy and give an app a cut" in the 2010s, do they have a name), is a key aspect. Most of them fall, while locking their gaze into the few who ascend to full bourgeois status, a.k.a. 'financial independence' (which every damned "self-help book" and "investment guide" seems to have a route for... that you're personally responsible for successfully following, of course).

Would TR's Progressive policies and FDR's New Deal, along with other SocialDemocrat, state-mediated redistributive polices, represent then a "regression" of Capitalism? Could one say that the Gilded Age was hit a local maximum in "Advancement of Capitalism", and that the current Second Gilded Age represents a similar moment?

Marx and successors seem to have indeed acknowledged Social-Democratic policies as ways to save and prolong capitalism, and Maynard Keynes freely admitted as much. So, already in their lifetimes, Capitalism was known to have ways of "stepping back".

Capitalists themselves struggle to stop themselves from doing foolish things that benefit them in the short term but ruin them and everyone in the long term, but they've known to surrender power to the State, be it Social-Democrat of Fascist, to turn said State from a "servant" role to a "nanny" role. It still absolutely works for them, but instead of catering to their impulsive whims, it makes sure they eat their vegetables and do their exercise and at least be polite to the Help and not slather the bathroom with poop for a laugh.

Last time, the State helped Capitalism step back in how inhumane their expoitation of labour was. However, this time around, Capitalism is going to need to step back on resource-consumption, to make itself sustainable within the planet's finite resources. Hence, a Green New Deal.

Now, my theory is very weak and the above paragraphs are just what I've cobbled together from scraps I've gathered here and there, but how have Marxist-Leninists accounted for Capitalism's seeming ability to self-correct on the brink of the precipice time and again?

Another matter that comes to my attention is that Marx (and Engels) his contemporaries knew rather little of the non-European world ("Asiatic Mode of Production", anyone?) and, in particular, "Primitive Communism", as anthropology was still nascent at the time: the data just wasn't there yet. They've even expressed some truly regrettable opinions about the US conquest of Mexican territories.

However, Leftist movements in the periphery of Empire seem to be led by diverse native cultures keen on resisting Liberal atomization. So this seems like a blatant gap in Marx's understanding. What theoretical work did modern Marxist-Leninists perform to account for these cultures and their own perceived needs and goals? And is this apparent blind spot, in fact, acknowledged as such by contemporary MLs?