as for the 'One,' 'Two,' bit, it's a way of speaking, (or thinking) that adds to the voice of the character. I wouldn't want a character to be so proper, even in thought, that it takes away from their idiosyncrasies.
I agree with that completely. The voice of the character is key--this is a story, not an article for a scientific journal or something.
I think it clarifies a bit.
On the contrary, it confuses the reader, because the modern convention is to use quotes for two things: (1) to indicate
speech, or (2) to indicate odd phrasing that the speaker/writer would not use him or herself. Example: Your so-called "man boobs" do indeed bounce wildly when you run. The use of quotes there indicates--probably for humorous effect--that the speaker would not normally elect to describe that part of the person's physique as "man boobs."
And of course, if the quotes surround an entire sentence instead of a short phrase, it denotes speech. So if you use quotes, the reader will wonder if he's talking--if he's actually speaking these thoughts out loud. That risks distracting and confusing the reader.
Talking quotes are encased by doubles (") and quoting quotes are encased by singles (') so, you could put it as though she is quoting her own thoughts. It sets it apart in a way that the reader could follow easily.
I'm not sure what you mean by "quoting quotes." The singles/doubles distinction is when a person speaking is, in part of what they say, quoting someone else. For example, a student talking to her friend might say: "I was talking to my teacher, and she said, like, 'You're at risk of failing this class.' I was like, totally? And she was like, 'Totally!'"
Or as in the example above--if it were in dialogue, it would look like this: "Your so-called 'man boobs' do indeed bounce wildly when you run." The speaker is quoting the other person--using the other person's language.
It's a quote within a quote, basically. So I'm not seeing how it relates to depicting the unspoken thoughts of a character.