If I were living at the time of the introspectionists, was there a better alternative for me? I suspect that unless I personally worked out some other theory (unlikely), I'd have to either take that one or something equally bad.

Once, for a Wittgenstein course, I read through the entirety of William James's 1890 Principles of Psychology. It was of course absurdly outdated, but I learned a lot from it. One of the things was surprise at how much time James felt he had to spend in the book attacking theories involving souls.

So yes, you could do much worse than being an introspectionist.