Single incipit bar for a staff group of two instruments

[Marcin Damianiak]

Dear All,

I'd like to ask for a little bit of help with the following matter:

What I'm trying to achieve is to make single centered incipit bar for the
staff group of two instruments. As for now, my code produces three
incipits; I tried omitting particular Staff.InstrumentName but it also
removes the shortInstrumentName, which is unwanted.

Here's my code:

\version "2.22.1"

incipit =
#(define-music-function (parser location incipit-music) (ly:music?)
  #{
    \once \override Staff.InstrumentName.self-alignment-X = #RIGHT
    \once \override Staff.InstrumentName.self-alignment-Y = ##f
    \once \override Staff.InstrumentName.padding = #1
    \once \override Staff.InstrumentName.stencil =
      #(lambda (grob)
(let* ((instrument-name (ly:grob-property grob 'long-text)))
  (set! (ly:grob-property grob 'long-text)
#{ \markup
     \score
        {
  { \context Staff \with {
                    } $incipit-music
  }
                  \layout { $(ly:grob-layout grob)
            line-width = \indent
                    indent =
                            #(primitive-eval
                                       '(or (false-if-exception (- indent
incipit-width))
   (* 0.5 indent)))
            ragged-right = ##f
            ragged-last = ##f
            system-count = #1
                  }
}
 #})
           (system-start-text::print grob)))
  #})

IandII.Incipit = <<
  \new Voice = "IandII.Incipit" <<
    {
      \set Staff.instrumentName = #"I and II"
      \clef G
      \time 4/4
      <g' c''>1 \bar ""
    }
  >>
>>

scoreI = \relative c'' {
  c1 \break c
}

scoreII = \relative c'' {
  g1 \break g

}

scoreIPart = \new Staff \with {
  %\omit Staff.InstrumentName
  shortInstrumentName = "I"
} \scoreI

scoreIIPart = \new Staff \with {
  %\omit Staff.InstrumentName
  shortInstrumentName = "II"
} \scoreII

\score {
    \new StaffGroup \with {
    instrumentName = ""
    \incipit \IandII.Incipit
    }
{ <<
    \scoreIPart
    \scoreIIPart
  >> }

  \layout {
  indent = 6\cm
  incipit-width = 3\cm
  }
}

Could you give me a hint how to get it right? Any help would be greatly
appreciated!

Best,
Marcin