Incipit: horizontal alignment of instrument names

[Johannes Roeßler]

Hi Group,

I've got issues with aligning the instrument names when using incipits.

A solution discribed here https://lilypondforum.de/index.php/topic,894.0.html help to some degree,
but my piano staff still doesn't fit.

\version "2.22.0"


altinc={ \clef "alto" \time 2/2 \key g\major b4 }

\score {
  <<
    \new ChoirStaff
    <<
      \new Staff = Soprano
      \with {
        instrumentName = "Soprano"      shortInstrumentName = "S"
      }
      {
        \incipit { \clef "soprano" \omit Staff.TimeSignature s1 }
        \repeat unfold 12 { c''4 c'' c'' c''}
      }

      \new Staff = Alto
      \with {
        instrumentName = "Alto"
        shortInstrumentName = "A"
      }
      {
        \incipit \altinc
        \repeat unfold 12 { c''4 c'' c'' c''}
      }

      \new Staff = Tenore
      \with {
        instrumentName = "Tenore"
        shortInstrumentName = "T"
      }
      {
        \incipit { \clef "tenor" \omit Staff.TimeSignature s1 }
        \clef "treble_8"
        \repeat unfold 12 { c'4 c' c' c' }
      }

      \new Staff = Basso
      \with {
        instrumentName = "Basso"
        shortInstrumentName = "B"
      }
      {
        \repeat unfold 12 { c''4 c'' c'' c'' }
      }
    >>
    \new PianoStaff
    \with {
      instrumentName = "Orgel"
      shortInstrumentName = "Org"
    } <<
      \new Staff = "right"

      {
        \repeat unfold 12 { c''4 c'' c'' c'' }
      }


      \new Staff = "left"

      {
        \repeat unfold 12 { c''4 c'' c'' c'' }
      }

    >>
  >>
}
\layout {
  indent = 5\cm
  short-indent = 1\cm
  incipit-width = 3\cm
  \override Staff.InstrumentName.self-alignment-X = #LEFT
}

Any advice?

Thx and best regards
Joei