It was common knowledge in the Christian community that John the Baptist baptized Jesus. If the words could be misunderstood to suggest that John did not baptize Jesus because he was already in prison, there were Christians who could put the reader straight. But as I said, I have seen this narrative device so many times in my own reading of novels and history that it is not that much of a problem to me.
Authors often tie up one topic with a neat bow that goes beyond the main time line of the narrative.
Afterwards they return to the main narrative time line. Authors expect the reader to be able to make these shifts. However, I thank you for all the citations which you give that show authors with your perspective, or with observations that can support your perspective. You are kind to supply them, and I knew that you could. I sympathize with the need to account for the text, but to read all sorts of things into it about Luke's embarrassment seems the machination of an overworked imagination to me.