Cheryl Schatz

Craig,
You said:

2. Also, as far as I am aware, 1 Tim 1:3 uses the Greek term for people, not just men.

You are correct that the Bible uses the term tis meaning anyone. The actual grammar of this word is masculine but this is the default grammar just as all passages speaking about salvation where “any man” follows Christ, all of these passages are generic but with the masculine grammar. This does not mean that only men can be saved and only men can follow Christ or only men were false teachers. It is rather a generic term meaning people just as you thought.