cross-staff-stem with stem down

[Helge Kruse]

I want to write a cross-staff-stem and used the pattern from the snippet 
repository. I managed to get the cross-staff at the second beat. But i 
would like to have the stem down.

When I try to change the stem direction I am not able to set correct 
duration. I think this breaks the cross-staff.

How do I get the stem down?

Regards,
Helge

PS: how do I remove the bar at the two last accords?



% Each measure should produce the same picture.
\version "2.16.0"

global = { \key g \major  \time 3/8 }

upper = \relative c'' {
  \global
<a fis>16[ <g e>] \autoBeamOff fis16 <e g,>16 <d fis,>8  |
<a' fis>16[ <g e>] \voiceTwo fis16 \oneVoice <e g,>16 <d fis,>8 |
<a' fis>16[ <g e>] \stemDown fis16 \stemNeutral <e g,>16 <d fis,>8
}

lower = \relative c' {
  \global
  \autoBeamOff
<d, d,>8 \crossStaff { \voiceOne <d a'>16 s \oneVoice } d8 |
<d d,>8 \crossStaff { \voiceTwo <d a'>16 s \oneVoice } d8 |
<d d,>8 \crossStaff { \stemDown <d a'>16 s \stemNeutral } d8 |
}

harpPart = \new PianoStaff \with { \consists #Span_stem_engraver }
<<
  \new Staff = "upper" \upper
  \new Staff = "lower" { \clef bass \lower }
>>

\score { \harpPart }