Hi Deb! A mixed up key signature can sometimes be a way of indicating that a piece has been written in a mode that is different from what we expect to hear in a major or minor scale.
Modal music is frequently written in a traditional key signature with accidentals used to raise or lower specific notes, but if a composer is expressing sounds as he wishes to do so using a key signature of one sharp and one flat, there is no local, state, or federal law preventing him or her from doing so. This is more familiar in folk and jazz and generally not so familiar in Traditional Western music, but even there, some composers during the past 100 or so years did some of this notation experimenting too.
Keep in mind though that the composer you mentioned may also have had something different in mind.
I’m not familiar with “the backward slash” but hopefully someone else will fill us in on that. I’d like to know too.