Considering the thrust of my comment, I don't understand the question. Obviously paraphrasing someone else's words into ones you like better is a fine and acceptable thing to do. So clearly I am just illustrating the problem by example.
The real answer is twofold.
1. We don't have a special 3rd kind of quote or other punctuation mark for reinterpreted references.
2. The real one: This is not a quote that lies as you imply. It is a new message, that merely uses quotes to denote a speaker, as in a pure fictional work, where the characters dialog is in quotes, even though no actual human was actually quoted.
Are there any other conundrums and baffling mysteries I can clear up for you?
When you use that syntax it looks like you are calling out an explicit quote; you may think that it's a reasonable paraphrase but I think most readers will see what you did as a strawman instead of a paraphrase.
Better to write inline "I feel like what you said amounts to [...]" to reduce the perception they you're making up quotes they someone didn't say or even clearly imply.
No one literate is in any danger of misinterpreting this very basic technique. I don't care about anyone else because it doesn't matter, they will misinterpret regardless, deliberately.
> Obviously paraphrasing someone else's words into ones you like better is a fine and acceptable thing to do.
Wrong. Not only is it tasteless and dishonest (not "fine"), it is against the rules of this site. But regardless of whether it's allowed elsewhere, you still shouldn't do it. (See "tasteless and dishonest".)
The real answer is twofold.
1. We don't have a special 3rd kind of quote or other punctuation mark for reinterpreted references.
2. The real one: This is not a quote that lies as you imply. It is a new message, that merely uses quotes to denote a speaker, as in a pure fictional work, where the characters dialog is in quotes, even though no actual human was actually quoted.
Are there any other conundrums and baffling mysteries I can clear up for you?