Vertical space above ossia

[Walter Garcia-Fontes]

I'm having trouble eliminating vertical space above an Ossia
snippet. This is the example of the manual, augmented to extend over
multiple lines:

\version "2.19.32"

\new Staff = "main" \relative {
\repeat unfold 4 {  c''4 b d c} \break
\repeat unfold 4 {  c4 b d c}
  <<
    { c4 b d c }

    \new Staff \with {

      \remove "Time_signature_engraver"
      alignAboveContext = #"main"
      \magnifyStaff #2/3
      firstClef = ##f
    }
    { e4 d f e }
  >>
\break
\repeat unfold 4 {  c4 b d c}
  c4 b c2
}

I had a demand to put the ossia closer to the below staff, and to
keep the distance between staffs the same. 

Looking for old posts I found this one that claims to achieve this,
but it only solves the first demand with the padding property:

http://lilypond.1069038.n5.nabble.com/Ossia-distance-unwanted-vertical-spacing-td206336.html

So this is how my snippet looks like with this:

\version "2.19.32"

\new Staff = "main" \relative {
\repeat unfold 4 {  c''4 b d c} \break
\repeat unfold 4 {  c4 b d c}
  <<
    { c4 b d c }

    \new Staff \with {

      \remove "Time_signature_engraver"
      alignAboveContext = #"main"
      \magnifyStaff #2/3
      firstClef = ##f
     \override VerticalAxisGroup #'default-staff-staff-spacing = #'(
(basic-distance . 0)
(minimum-distance . 0)
(padding . 1.5)
(stretchability . 90) )
    }
    { e4 d f e }
  >>
\break
\repeat unfold 4 {  c4 b d c}
  c4 b c2
}

The vertical distance above the ossia I could not reduce no matter how
much I tweaked the numbers in the override, and so the distance
between the two lines with ossia in the middle is different from the
rest. I also tried "staff-staff-spacing" instead of
"default-staff-staff-spacing" but there is no change.

Is it possible to reduce the vertical distance above the ossia? I
gave up and ended up doing the ossia with music included in a markup,
for the markup I know how to tweak all vertical distances.

-- 
Walter Garcia-Fontes
L'Hospitalet de Llobregat