Is there a way to do a quote:
inline similar to
While attempting, > This doesn't work > or > this <
I want to bring attention to my inline quote, and I don't feel quotations marks are enough.
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Yes, quotation marks. That's what they do.
If you want to quote something so short that it should be inline you probably just want to wrap it in quotation marks. Otherwise, if you're actually quoting something substantial, it should be a block-level element.
Wikipedia tells us that "in English writing, quotation marks ... are punctuation marks surrounding a quotation, direct speech, or a literal title or name", which sounds very much like what you're looking for.
As far as something more visually distinct, frankly, we need less bolding/italicizing/inline styles. There is absolutely no reason to mark some parts of your post more important than others. You should be stripping out the unimportant parts until only the important parts remain. Whatever quote you're inserting shouldn't require any special visual styles to stand out; if your question is written properly and of a reasonable length, people will read the quote in the course of reading your question.
If you're worried about your quote getting lost, you're filling your question with too much fluff. You should pare it down until there is literally nothing left for you to remove without changing the meaning of the question.