Throw the cow over the fence some hay. What did you bring that book that I didn't want to be read to out of up for?> What did you take the car driving the man who brought the book that I didn't want to be read to out of up away in for?
Almost-untangled form:
> For what reason did you take in the car driven away by the man who brought up the book that I did not want anyone to read words out of [the book] to me?
Although if you are being very specific, I think some syntacticians might treat the "out" in "out of" and the "up" in "bring up" as a different word classes than normal prepositions (the "out" is modifying another preposition's direction, and the "up" is a particle in a phrasal verb [1]). And I think that's one of the reasons the original form is so compelling is that you have some variance in form giving you clues -- the directional modifier, the question-inversion/wh-fronting, the salience of "bring up" -- that make it tantalizingly close to natural. Whereas mine just becomes a churn of words, at least in my reading.
[1] https://en.wikipedia.org/wiki/Phrasal_verb#Examples_of_Phras... (see the notes on distinguishing between particle & prepositional phrasals)