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I'm not too sure what this 得 is doing here. If I rewrite as in 2. or 3. is that a) correct and b) still the same meaning?
Basically, I'm not sure what 空前绝后 is describing. Either 极端 or 假设， or both?
I would translate the phrase as: Derek Parfit presents the extreme（极端） and unprecedented（空前绝后） hypothesis that,
It is not good English to write 'extremely unprecedented'. Either something is unprecedented, or it is not.
For 极端得空前绝后的假设, 空前绝后 is describing 极端, to express the degree of 极端. And 极端 is describing 假设. So 极端得空前绝后的假设 could be parsed as 极端（得空前绝后）的假设, means (unprecedentedly) extreme hypothesis.
And when describing the degree of verb/adj, 得 should be used.
Note that in the 2nd sentence, if you change 得 to 的, the syntax is valid but the meaning changes; it becomes 极端的，空前绝后的假设, both 极端 and 空前绝后 describe 假设, means extreme and unprecedented hypothesis.
For the 3rd sentence, I'll say that using 地 is wrong syntax here.
Here're some references about the differences among 的, 地, 得:
「的、地、得」的用法有何区别？
“的、地、得”的用法
The answer provided by @songyuanyao seems to be correct for me.
I'll show you how to Let's use x-bar theory to decompose the sentence.
Sentence = 德里克.帕腓特有一个极端得空前绝后的假设 Sentence = Noun Phrase(德里克.帕腓特) + Verb Phrase(有一个极端得空前绝后的假设)
Noun Phrase(德里克.帕腓特) = Noun(德里克.帕腓特)
Verb Phrase(有一个极端得空前绝后的假设) = Verb(有) + Noun Phrase(一个极端得空前绝后的假设)
Noun Phrase(一个极端得空前绝后的假设) = Determiner(一个) + Adjective Phrase (极端得空前绝后的) + Noun(假设)
In serious writing, you should never misuse 的,地 and 得.
的 is used between an adjective phrase and a noun phrase which the adjective phrase is describing.
地 is used between an adverbial phrase and a verb phrase which the adverbial phrase is describing.
得 is used between a noun phrase or a verb phrase and the complement which is describing the previous phrase.
No.3 德里克.帕腓特有一个极端地空前绝后的假设…… also doesn't work well in Chinese. Although it can be reasonably analyzed, but it is not a usual way to say. The reason is like the one you gave for English.
No.1 德里克.帕腓特有一个极端得空前绝后的假设…… can even have two ways to understand:
空前绝后 is describing 极端
Both describing 假设. This may sound strange but it is more obvious with another example:恐怖得可以吓死人的某物(Something terrifying enough to scare people to die). Both 恐怖 and 可以吓死人 are describing the noun.
So, with the context, it could mean 'unprecedentedly extreme hypothesis' or 'hypothesis which is extreme enough to call it unprecedented'
(1) 极端得空前绝后的 = unprecedentedly extreme
(2) 极端的，空前绝后的 = extreme and unprecedented
It depends which you want to express. (They seem similar to me.)
I'd say (3) is unacceptable. 极端地 is an adverb that modifies a verb, but there is no verb.
What I said corresponds with my memory of high-school textbook. Keep in mind that Chinese usage is far from uniform, and don't be surprised if you find something different from your books. Purist will hold that (3) is wrong, but many laypeople might be okay with that.
