Note that "run the gamut" begins with the word "run". "Run" is a verb and normally requires a subject. While "run the gamut" is a specific idiom, it does not break this rule.
Normally in English the subject comes before the verb. So we would expect to see "[subject] runs the gamut ...", i.e. some subject coming before the word "run". Like, "Posters on ELL run the gamut from Americans to Britons to Indians to people from countries where English is not commonly spoken at all."
That said, English word order is not totally inflexible. You can write sentences that vary it, usually for emphasis or poetic style. For example, "Running the gamut from Americans to Japanese, posters on ELL are a diverse group."
Imperative sentences have an implied subject of "you", and so often begin with a verb. Like, "Run away!" But an imperative sentence using "run the gamut" seems unlikely.
Your example sentence doesn't make much sense to me. Who or what is running the gamut here? It is not the subject of the second clause, "laws". Laws do not run the gamut from nomadic tribes to skyscraper cities. Those aren't kinds of laws. The sentence mentions "societies". Those could be kinds of societies.
I think the writer meant something like, "In societies running the gamut from nomadic tribes to skyscraper cities, laws were central pillars in making them function."
All of the adjectives you have suggested can be used to modify "distance," although all except "much" require the indefinite article, as in "a huge distance," "a large distance," "a long distance," and "a big distance."
Please note that "shallow" can also be applied to a person, meaning, "someone who is superficial, intellectually unsophisticated, primarily interested in material possessions," and so forth.
Best Answer
I think the word you're looking for is long-term. We refer to long-term benefits or long-term goals. Long run would make more sense like this:
Long-term is hyphenated because it's a compound adjective. The long run is not; I'm pretty sure it's a noun phrase.