I think Vines’ book is reasonable. But I have two caveats:
1) He assumes that Rom 1 is Paul’s view. I think Paul starts the book by quoting the view he’s responding to. That’s part of “diatribe style,” which most commentators think Romans uses.
There are at least 2 reasons to think that. First, Rom 2:2 quotes 1:32 and rejects it.
Second, the argument makes more sense with it as the opposing view. The usual exegesis is that Rom 1 - 3 is demonstrating first the sinfulness of Gentiles and then the sinfulness of Jews. But the issue that Paul is dealing with is acceptance of Gentiles. 1 is the classic attack on this. Because of idolatry, Gentiles are inherently immoral. But why in Rom 2 does he talk about Gentiles with the Law written in their hearts? That doesn't make sense with the usual understanding. It makes a lot more sense if 1 is the view he objects to. Then he has two responses. In Rom 2, no, Gentiles are not inherently immoral. Some have the Law written in their hearts. In Rom 3, Jews aren’t angels either.
2) There’s lots of discussion about arsenokoitai. I agree with him the defining a word from its roots, without enough usage to see how it was used, is dangerous. The argument for derivation from Lev is strongest if Paul invented it. But a number of scholars think the use in the Sybyllines is independent. In that case he didn’t invent it. Vines’ argues from the position of the word in sin lists. It’s an interesting suggestion, but hardly proof. I think NRSVue is probably right to punt. They translated it “men who engage in illicit sex.” Paul surely had something more specific in mind, but that’s all we can be sure of.