Hi Federico,

I’ve adjusted my snippet a little, and I think it might handle all your spacing 
issues…? Let me know!

Best,
Kieren.

%%%  SNIPPET BEGINS
\version "2.25.15"

\paper {
  system-system-spacing.padding = 4
}

\layout {
  \context {
    \type "Engraver_group"
    \name TS
    keepAliveInterfaces = #'( time-signature-interface )
    \consists "Time_signature_engraver"
    \override TimeSignature.font-size = #-1
    \override TimeSignature.extra-offset = #'(-1.75 . 1.25)
    \consists "Axis_group_engraver"
    \override VerticalAxisGroup.staff-affinity = #UP
    \override VerticalAxisGroup.nonstaff-relatedstaff-spacing =
      #'((basic-distance . 3) (minimum-distance . 2) (padding . 1))
  }
  \context {
    \type "Engraver_group"
    \name ScoreMarks
    keepAliveInterfaces = #'( metronome-mark-interface time-signature-interface 
)
    rehearsalMarkFormatter = #format-mark-box-alphabet
    \consists "Axis_group_engraver"
    \override VerticalAxisGroup.staff-affinity = #DOWN
    \override VerticalAxisGroup.nonstaff-relatedstaff-spacing =
      #'((basic-distance . 3) (minimum-distance . 2) (padding . 1))
    \consists "Metronome_mark_engraver"
    \override MetronomeMark.Y-offset = #0
    \override MetronomeMark.X-offset = #2
    \override MetronomeMark.outside-staff-priority = #50
    \override MetronomeMark.break-align-symbols =
      #'(left-edge staff-bar clef time-signature key-signature)
    \override MetronomeMark.non-break-align-symbols =
      #'(paper-column-interface)
    \override MetronomeMark.extra-spacing-width = #'(0.5 . 0.5)
    \consists "Mark_engraver"
    \override RehearsalMark.Y-offset = #0
    \override RehearsalMark.outside-staff-priority = #100
    \override RehearsalMark.break-align-symbols =
      #'(left-edge staff-bar clef time-signature key-signature)
    \override RehearsalMark.self-alignment-X = #CENTER
    \override RehearsalMark.extra-spacing-width = #'(0.5 . 0.5)
    \consists "Text_spanner_engraver"
    \override TextSpanner.font-size = #2
    \consists "Time_signature_engraver"
    \override TimeSignature.font-size = #-1
    \override TimeSignature.X-extent = #empty-interval
    \override TimeSignature.X-offset = #-1.75
    \override TimeSignature.extra-offset = #'(0 . 1.5)
  }
  \context {
    \Score
    \remove "Bar_number_engraver"
    \remove "Metronome_mark_engraver"
    \remove "Mark_engraver"
    \accepts ScoreMarks
    \accepts TS
  }
}

tsIn = {
  \undo \omit Staff.TimeSignature
  \omit ScoreMarks.TimeSignature
  \omit TS.TimeSignature
}
tsOut = {
  \omit Staff.TimeSignature
  \undo \omit ScoreMarks.TimeSignature
  \undo \omit TS.TimeSignature
}

global = {
  \once \omit ScoreMarks.TimeSignature
  \once \omit TS.TimeSignature
  \time 4/4 s1
  \tsOut \tempo "Allegro" \time 3/4 s2.
  \tsIn \time 6/8 \tempo "Adagio" s2.
  \tsOut \time 2/4 \tempo "Allegretto" s2
  \tsIn \time 2/2 s1
  \tsOut \time 6/4 s1.
  \tsIn \time 4/4 s1
  \time 3/4 s2.
}

someNotes = \repeat unfold 58 { c'8 }

\score {
  <<
    \new ScoreMarks \global
    \new StaffGroup <<
      \new Staff = "one" \new Voice { << \global \someNotes >> }
      \new Staff = "two" \new Voice { << \global \someNotes >> }
      \new Staff = "thr" \new Voice { << \global \someNotes >> }
    >>
    \new TS \global
  >>
}
%%%  SNIPPET ENDS

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