LilyPond double stems across staves

LilyPond double stems work fine across staves.

   \new PianoStaff <<
      \new Staff = RH {
         \time 4/8
         c''8 [ c''8
         \change Staff = LH
         <<
            { e'8 }
            \new Voice { \once \override Stem #'direction = #down e'8 }
         >>
         \change Staff = RH
         c''8 ]
      }
      \new Staff = LH { s2 }
   >>

The trick is in instantiating the parallel music << >> construct with no \\ separator between the first expression { e'8 } and the second { \once \override Stem #'direction = #down e'8 }.