Still about the filler word 很, after 得 I just learned that an adverb or quality describing how a verb (action) is performed must be preceded by the filler word 得, which introduces an &quot;expression of degree&quot; (&quot;well&quot;, &quot;badly&quot;, &quot;quickly&quot;, etc.).
But, while 得 occurs immediately after the main verb, it does not necessarily precede the descriptive quality directly. If the quality describing the first verb is conveyed by a descriptive verb (or adjective-verb), it seems that 很 must always precede the descriptive verb in simple affirmative sentences, provided that no additional emphasis of the quality is given. As such, if I understood correctly:
她说得好吗? - Does she speak well? (interrogative sentence, no 很)
她不说得好。- She does not speak well. (negative sentence, no 很)
她说得那么好。- She speaks so well. (no 很 here, since 那么 replaces it as the emphasis)
她说得很好。- She speaks well. (simple statement with minimal description, 很 required)
得-adverbs are a type of complement (補語). They

modify verbs or adjectives;
by definition follow the word to be modified; and
can be made out of various syntactical items (i.e., not necessarily a simple adjective like 好).

This website provides four examples (interrogative pronoun, adjectival phrase, verbal phrase, and topic-comment phrase respectively) to illustrate the third point:

休息得怎麼樣？（代詞）How are you resting?
做得挺好（形容詞性詞語）(You) did rather well.
凍得直哆嗦（動詞性詞語）(I was) so cold that I trembled.
高興得大家又唱又跳（主謂詞組）Everyone was so elated that they sang and danced.


Regarding negative sentences (your second example), the logic in Chinese is slightly different from that in English: 不 is treated somehow like an adverb that closely modifies the adjective when negating it. So it goes into the 得-phrase, not the other way round:

她說得不好。(lit. She speaks not well.)
*她不說得好。


While your third example is grammatical (i.e. you violated nothing regarding 得-constructions), it does not sound right (so this is not a problem of grammar but of word choice). Mostly because 那麼 does not exactly mean 'so' – a closer English approximate is the adverb 'that'.

i. 她說得不那麼好。 She doesn't speak that well.
ii. 她說得那麼好嗎？ Does she speak that well?
iii. 既然她說得那麼好，你就選她當司儀吧。 Since she speaks that well, why don't you choose her as the emcee?
iv. ?她說得那麼好。 ?She speaks that well.

Usually there is a hidden reference when we use 那麼. In i., she does not speak that well when compared to the standard you expect her to speak with. In ii., the asker is doubting if she really speaks that well, presumably after hearing what others say about her speaking. In iii., she speaks with such a standard that she qualifies to become an emcee. In iv., however, there is no suitable context to justify the use of 那麼.

Your observation on 很 in 得-phrases is alright. There is nothing to fault in your explanation for your fourth example.

Just a minor point: you may hear people exclaim 說得好！ ('Well said!') or have come across the phrase 俗話說得好 ('as the saying goes', lit. folk saying says it well). They usually don't include 很. There is generality in these sentences (so they are, in Zhu Dexi's terms, type I constructions, as per my second point here).