Reading all this I can't get the phallic motif out of the imagery because, quite specifically, of the word "jack".

If it's Blues and looks like innuendo, then it is innuendo. IMNSHO

If there are several meaning to be gleaned and it's a lyric, then those meanings support the wider appeal of the song. And often they are all there because they were put there. But not always, as I found with some of my songs, but mostly.