Working a bit on Jeffery’s suggestion, it seems to be getting very close to 
what you want:

\version "2.18.2"
\markup \vspace #3

beamPos =
#(define-music-function
  (parser location beg end)
  (number? number?)
  #{
    \once \override Beam.positions = #(cons beg end)
  #})

musOne = {
  <<
    \new Staff = "first" {
      <<
        \new Voice = "one"
        {
          \voiceOne \stemUp
          c'''16[ d''' c''' d''' c''' d''' c''' d'''
          \change Staff = "second"
          d'']
        }
        \new Voice = "two"
        {
          \voiceTwo \stemDown
          s2
          \once \override Rest.transparent = ##t
          \beamPos -4 -4
          r32[ 
          \set stemRightBeamCount = #2
          c''' 
          \change Staff = "second"
          \once \stemUp
          \set stemLeftBeamCount = #2
          \set stemRightBeamCount = #3
          gis''32 
          \change Staff = "first"
          d'''16 c''' d''' 
          \set stemRightBeamCount = #1
          c'''32 
          \change Staff = "second"
          \once \stemUp
          \set stemLeftBeamCount = #1
          d'' 
          \change Staff = "first"
          c''']
        }
        \new Voice = "three"
        {
          s2
          s16
          \change Staff = "second"
          \stemUp

          \override Stem.cross-staff = ##t
          %\override Voice.Stem.length = #30
          
        }
      >>
    }
    \new Staff = "second" {
      
      s2
      s16
      \stemDown
      \tupletDown
      
      \tuplet 5/4 {
        gis''16[ dis'' cis'' dis'' cis''] 
      }
      d''16
    }
    
  >>
}


\score {
  \musOne
  \layout {
    \override NoteHead.stem-attachment = #'(0 . 0)
    \context {
      \Score
      proportionalNotationDuration = #(ly:make-moment 1/64)
      \override SpacingSpanner.uniform-stretching = ##t

    }
  }
}


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