Term for sentences using multiple repeated words

The word that comes closest to describing this sort of behavior(repetition of the same word in a sentence) is: Epizeuxis

According to Wikipedia:

In rhetoric, an epizeuxis is the repetition of a word or phrase in immediate succession, for vehemence or emphasis.

Some examples provided(among others):

• "Never give in — never, never, never, never, in nothing great or small, large or petty, never give in except to convictions of honour and good sense. Never yield to force; never yield to the apparently overwhelming might of the enemy." —Winston Churchill

• "O horror, horror, horror." —Macbeth

• "Words, words, words." —Hamlet

• "Rain, rain, rain, rain, rain." —Guy Gavriel Kay

• "Developers, developers, developers, developers, developers, developers. Developers, developers, developers, developers, developers, developers, developers, developers!" —Steve Ballmer

• "Never, never, never, never, never!" —King Lear

• "But you never know now do you now do you now do you." —David Foster Wallace, Brief Interviews with Hideous Men

However, do note this in the definition of Epizeuxis:

for vehemence or emphasis

It appears this sort of repetition is usually done to emphasize some meaning. Accordingly, I'm not sure if a sentence like:

That that exists exists in that that that that exists exists in.

would classify, without any further context.

But then again, upon reading the answers in your cited EL&U questions, it looks like these sentences do make sense. In that case, I would say "Epizeuxis" is indeed the word you're looking for.

Also take a look at Repetition as defined on Wikipedia. There seem to be some other types of repetitions which you might be interested in:

• Conduplicatio is the repetition of a word in various places throughout a paragraph.

  "And the world said, 'Disarm, disclose, or face serious consequences'—and therefore, we worked with the world, we worked to make sure that Saddam Hussein heard the message of the world."(George W. Bush)

• Mesodiplosis is the repetition of a word or phrase at the middle of every clause.

  "We are troubled on every side, yet not distressed; we are perplexed, but not in despair; persecuted, but not forsaken; cast down, but not destroyed..." (Second Epistle to the Corinthians)

• Diacope is a rhetorical term meaning uninterrupted repetition of a word, or repetition with only one or two words between each repeated phrase.

"Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo." (covered here)

In The Etymologicon: A Circular Stroll through the Hidden Connections of the English Language, author Mark Forsyth cites this very Buffalo sentence and the Mandarin "Shi shi" poem as examples of Antanaclasis.

According to Wikipedia, Antanaclasis is:

"... the literary trope in which a single word or phrase is repeated, but in two different senses."

Merriam-Webster's definition of antanaclasis is similar:

"the repetition of a word within a phrase or sentence in which the second occurrence utilizes a different and sometimes contrary meaning from the first."