I'll provide a tentative answer that isn't supported by any scientific research I'm aware off, only my own observations as an autodidact History student, so take it with several grains of salt. With that disclaimer in place, here's a hypothesis I've been nurturing for a few years already.
My insight takes as its main premise the fact traditional societies have organized in a hierarchical pattern that, in its broad strokes, varies little between places and times. This structure usually has four main classes, sometimes less, sometimes more, but when the number varies its usually either because two of the four are considered as one, or because sub-types of one are distinguished as their own individual classes. Additionally, the means of access (or lack thereof) to those classes, aka class mobility, vary a lot, ranging from self-attribution, to rigid by-birth caste rules, and passing through lots of other options, including meritocratic-like assignment via standardized tests, as was and remains the practice in China. Myself, I look at these classes as a broad way of classifying people in light of their psychologically-motivated core goals.
The four classes are:
a) Those who seek power, with a strong will to rule others, and set the rules others must follow.
Someone with this psychological profile this doesn't care for wealth, although wealth may be come as a side-effect of their exercise of power.
They feel fine if they're poor but are obeyed.
Abstract and pure knowledge doesn't appeal to them, if they need to know something they ask a summary from those who know.
b) Those who seek wealth, with a strong will to take calculated risks if the payoff is worth it.
Someone with this psychological profile doesn't care for power, although power may be, for them, a means to wealth, and so they may go for it.
They feel fine if they're as wealthy as possible, and even more so if their risk taking pays off in the form of even more wealth.
Their take about knowledge is similar to that of "a".
c) Those who seek knowledge and/or wisdom, with a strong will to learn as much as possible.
Someone with this psychological profile doesn't care for either power or wealth and prefer to avoid dealing with those at all if possible, although in the real world it's unavoidable, so they face the need to deal with both the powerful and the wealth lest their pursuit of knowledge is hindered.
They feel fine if they're learning, and respected for their knowledge. This may come in the form of dogmatic knowledge (think a religious theologians or jurist) or in an open minded, contrarian way (the kind of intellectual the first would hate, and vice-versa).
When dealing with "a" or "b", they either work for them, or are persecuted by them, but rarely want to exercise either kind of power. If they do so, it's by necessity, as a means to secure their access to learning. Usually their power, if any, is indirect, by means of setting the stage within which both "a" and "b" think.
d) Those who seek stability and safety, with a strong will to resist anything that might imperil these.
Someone with this psychological profile doesn't care for holding power, and neither for the risk taking involved in pursuing great wealth. They seek a stable life, within the boundaries of socially accepted mores, and the knowledge they pursue is for the practical uses of their profession, or a hobby.
They feel fine when they're respected by their community, for their work, and feel the finest when things work exactly as they've always worked. Changes, particularly quick, broad changes, stress them out. Therefore, they're usually conservative, but not in an ideological way, in a practical way.
When dealing with "a" or "b", they tend to obey as long as they don't feel their safety and stability threatened. When dealing with "c", they tend to agree if what they're hearing fits with their worldview, or to disagree in varying degrees of incisiveness when what they're hearing challenges their worldview. They're accepting of change if and only if it's brought slowly, and only if there's a clear benefit for their safety and stability, or at the very least no downside for them and theirs.
These are the four classes/castes typically found in traditional societies all over the world. At least, those I read about do fit, with minor variations.
So, let's take this, assume these classes are invariant, meaning that no matter how much society changes there will always be people whose deep psychological profiles are such that they follow these four end-goals, and contrast that with Libertarianism.
i) For type-a individuals, Libertarianism is something they clearly don't want. A minarchist society is one in which their power is severely reduced, while what they seek is to maximize it.
This fits with your Elite Support Hypothesis.
ii) For type-b individuals, Libertarianism is an "it depends" proposition. They don't care much about the principles, but they do care about the consequences:
If Libertarianism is implemented in such a way that doesn't prevent unrestricted wealth growth, including monopolization efforts, then they're for it in that specific context.
If Libertarianism challenges their wealth-seeking and the payoff of their risk-taking, they're against it.
And even if they at first are for it, but later conditions change and suddenly Socialism becomes the way for them to grow their wealth, that's what they'll go for.
So, this both fits and doesn't fit with your Elite Support Hypothesis.
iii) For type-c individuals, being for or against Libertarianism is a matter of intellectual preference. Some are drawn to it, some aren't, some are disgusted by it. It depends on how it fits or doesn't fit their other intellectual interests and preferences, specially if Economics isn't their main field of study.
As a rule of thumb, I venture type-cs tend to be anti-Libertarian in practice because in a minarchist society there are way less possibilities of dedication to pure intellectual pursuits compared to scenarios in which the State funds them without requiring immediate practical applications to arise from that funding. Sure, some type-cs have interests so well aligned with those of type-bs in their business capacity that they will always easily find corporate R&D funding, but for the majority of type-cs it's either going for type-as good will (public-funded research, government grants); for type-bs prestige support (tenured positions in private universities, partisan-NGO/think tank positions etc.); for type-ds direct support (acting sage/priest, journalism, infotainment host etc.); or giving up and going for a soul-crushing type-b or type-d lifestyle.
So, this both fits and doesn't fit, but mostly fit, with both your Elite and Non-Elite Support Hypothesis, as type-cs may be one, the other, both, or none, depending on context.
iv) Finally, for type-d individuals, Libertarianism is a downright scary thing, as Libertarianism embraces constant change on a massive scale as a very positive value, which goes against type-ds seeing constant, big changes as a safety hazard full of the very risks that must be avoided.
This fits your Non-Elite Support Hypothesis.
In summary, I'd say Libertarianism is more likely to be preferred by type-bs, and opposed by types a, c and d.
As for other economic systems, they have different distributions. Taking into account the Economics schools I've studied at least a little about, this would result in this table, with "+", "-" and "0" meaning, respectively, "in favor of/advantageous to", "opposed/disadvantageous to", and "neutral/indifferent towards", and exclamations meaning "see below":
- Mainstream: A+, B+, C+, D0
- "Europeanism"(!): A+, B0, C+, D+
- Libertarianism: A-, B(!!), C-, D-
- Marxism: A+, B-, C+, D(!!!)
- Distributism(!!!!): A-, B-, C-, D+
(!) I group in this things like European-style Social Democracy, Northern-European countries' brand of Capitalistic Socialism, US-style Liberalism (known elsewhere as Social-Liberalism), German-style Ordoliberalism etc. Or, to put it another way, big State, big corporations, huge taxes, big welfare state.
(!!) "+" for the majority of small players, "-" for the big ones.
(!!!) "+" if it's already established, "-" if it isn't and it'd require major societal changes, "0" otherwise.
(!!!!) Disclaimer: my own preference.
I hope this helps, and I'm all ears (eyes) for criticisms.
EDIT: Replaced exclamation marks for asterisks, as Markdown was turning those into italics and bolds.