Placing beam between staves with autochanging voice in LilyPond

Question

I have a PianoStaff with two voices on the right hand. The lower voice with eighths is spread across the staves with \autochange and the additional pitch parameter nicely controls the turning point.

However, the beam of the eighth notes is placed below the left hand staff which doesn't look very nicely.

There are similar questions about this topic here but they didn't help me with the issue. I strongly prefer \autochange as manual changes can become somewhat tedious. How can I put the beam between the staves as indicated in blue?

Here's the code:

\version "2.19.83"
\score {
  \new PianoStaff
  <<
    \new Staff = "up" {
      << 
        {
          \relative c' { \clef bass <g b d>2 <g b> }
        }
        \\
        {
          \autochange b, { d8 g, d g, d g, d g, }
        }
      >>
    }
    \new Staff = "down" {
      \clef bass
      \new Voice {
        \relative c, { g1 }
      }
    }
  >>
}

Answer 1

You need to restore the default stem direction with \revert Stem.direction because the notes are in a voice that has set the stem direction to DOWN. Use this:

\version "2.19.83"
\score {
  \new PianoStaff
  <<
    \new Staff = "up" {
      << 
        {
          \relative c' { \clef bass <g b d>2 <g b> }
        }
        \\
        {
          \revert Stem.direction                      % <--- added
          \autochange b, { d8 g, d g, d g, d g, }
        }
      >>
    }
    \new Staff = "down" {
      \clef bass
      \new Voice {
        \relative c, { g1 }
      }
    }
  >>
}

Resulting in: