I can only speculate
I have not as of writing this voted on the question or the answer you gave. However, I do believe I can answer some points as to "why" you are getting down voted.
First, the answer you cite for distinction of exegesis and hermeneutics is not the best of answers. This answer to a slightly different question is much better, and I would agree with its summary more than what you noted above (emphasis in original):
Basically the distinction boils down to this (as it pertains to the
Bible*): Hermeneutics is the field of study concerned with how we
interpret the Bible. Exegesis is the actual interpretation of the
Bible by drawing the meaning out of the Biblical text.
Exegesis is in close association to Hermeneutics, and both are dependent upon the Text itself, and all three are very on topic for the site. So when you object (above):
This wonderment is clearly related to the questioner's lack of
understanding of some aspect of the Greek language, which surely would
be better resolved by asking a question in a different place.
No, this is the right place. Original language questions related to a particular text are directly on topic, because resolving language aspects of the text are foundational to interpreting it. Likewise, translation issues from the original language to the target language are also directly on topic for the site, because we deal with the text in both original and (English at least) translations. Hence, the upvotes on the question. It was well stated as to the issue and the issue is directly related to topics on the site.
Second, one aspect of key importance in answering a question is to actually answer the question. There are two questions posed by the OP:
- The Title Question: "Where does 'by the mercy shown to you' belong in Romans 11:31?"
- The Sub-Question: "Can anyone outline and/or point me to a discussion of the grammatical points that favor understanding τῷ ὑμετέρῳ ἐλέει as part of the ἵνα clause?"
- Gives no resource information to answer the sub-question at all. Had you provided a very detailed discussion yourself about the aspects related to the grammatical and syntactical issues of determining its relation to the ἵνα clause, such that your own answer became itself a good resource, then lack of pointing to other resources would be okay (i.e., if people can see you know your grammatical/syntactical "stuff" and can walk the person through the logic of the issues about where it should be placed in translation).
- You sort-of answer the title question, as you take a position that it should be placed where the KJV places it, which is "after" the ἵνα clause. But you do not give a grammatical/syntactical explanation as to "why," which relates back to not answering the sub-question. But additionally, you give the parsing of the word order correctly, which shows the phrase in question before the "in order" (the parsed translation of ἵνα), and then you give the KJV rendering which puts it after the "that" (the KJV translation of the ἵνα). So your examples contradict order, but again, you do not explain the reasoning the translations that do that are doing that.
You also state:
Surely, the sensible approach to translation has to be: big picture
first, then the minutia.
I cannot speak for others, but I myself would disagree. You have to get the minutia of grammar/syntax structure of the original language correct first in order to properly translate a passage to a target language. The big picture comes into play for understanding the meaning of translated passage only after that passage is cleared as being properly translated from the original language.
Answering your direct question
So the first two points for sure, and possibly the third point as well, I am quite certain are the reasons for most/all the down votes. If I were to vote, as it stands, I would also upvote the question (because it is on topic, well stated, and clear) and downvote your answer (because of the above points). You did say some good contextual points that are relevant to the overall meaning of the verse, which are not bad points of themselves, but the fact that you did not address the primary points relevant to the questions asked makes those contextual points mute.
Third, I would comment also on a comment you made which would technically not be relevant to why you got downvotes, but is relevant to understanding the BH.SE site. You state:
This is not an academic community. It is
a Q & A site.
Which is in reply to part of this comment (emphasis in original):
A.) Please be respectful of people in our community.
Accusing people of being "bogged down in in the minutia of Greek" - is
inappropriate. B.) This is an academic community, not a religious
organization; When we want to discuss topics outside of the "minutia
of what the texts actually say" - we use other sites;
I would say neither of you are quite correct in statements made in that exchange.
- Against your statement, we are a Q & A site/community that seeks to have answers in an academic form (this answer does well to reflect that; but also see the question and upvoted answers here), and so we are attempting to function more like an academic community in the format of answers (especially) and questions (somewhat, though with more leniency).
- Against elika's statement, we are dealing with religious texts and the interpretation of those, and so while we are correctly "not a religious organization," we do deal at various levels with "topics outside of the 'minutia of what the texts actually say,'" for the "big picture" (to use your terms) becomes relevant at various levels, depending on the particular question and depending on the particular hermeneutical approach of an answerer.
So in short, I would classify BH.SE as a Q & A site/community that seeks to operate by academic standards from a variety of presuppositional1 and hermeneutical2 viewpoints when answering questions about the Biblical texts important to various religions/denominations.
1 Because BH.SE is not a Christian only site, there is a baseline presupposition in community people of theistic vs. atheistic approach to the texts. There is also various views on the level of natural vs. supernatural involvement in the production and preservation of the texts themselves. I could go on, but the point is that one needs to (a) be able to operate within this inclusive format by being civil, even if disagreeing with others views; and part of being civil would probably not include what a few have apparently taken as a cavalier dismissal when you state: "Focussing on the minutia of the Greek language can blind one to the substance of what is being communicated" (i.e., you feel the wrong question is being asked), and (b) not necessarily expect people to relate to a short quip such as your answer gives: "Paul's Olive tree analogy says precisely this." Many people from their background would have no clue what you meant by that.
2 For a list of some various types of hermeneutics, see the one provided in this answer.