consistentlyLeftAlignedBarNumbers = {
  \override Score.BarNumber.break-visibility = #end-of-line-invisible
  \override Score.BarNumber.self-alignment-X =
    #(lambda (grob)
       (let ((break-dir (ly:item-break-dir grob)))
         (if (= break-dir RIGHT) RIGHT LEFT)))
}

\new ChoirStaff <<
  \new Staff {
    \relative c' {
      \set Score.barNumberVisibility = #(every-nth-bar-number-visible 3)
      \bar ""
      \consistentlyLeftAlignedBarNumbers

      \set Score.currentBarNumber = #112
      \repeat unfold 8 { R1 }
      \break
      \repeat unfold 9 { R1 }
      \break
      \repeat unfold 7 { R1 }
    }
  }
  \new Staff {
    \relative c' {
      \repeat unfold 24 { R1 }
    }
  }
>>

\layout {
  indent = #0
  ragged-right = ##t
  ragged-last = ##t
}