For example, the following ALMOST does the right thing already, by simply 
combining the two contexts and adjusting the MMR number Y-offset:

%%%  SNIPPET BEGINS
%#(ly:set-option 'debug-skylines #t)
#(layout-set-staff-size 18.5)

\layout {

 \context {
   \Staff
   \name customStaffDown
   \alias Staff
   \inherit-acceptability customStaffDown Staff
   \omit MultiMeasureRestNumber
   \override MultiMeasureRest.expand-limit = #1
 }

 \context {
   \Staff
   \name customStaffUp
   \alias Staff
   \inherit-acceptability customStaffUp Staff
   \accidentalStyle piano
   \omit MultiMeasureRestNumber
   \override MultiMeasureRest.expand-limit = #1
 }

 \context {
   \name PianoMMR
   \type "Engraver_group"
   \inherit-acceptability PianoMMR Dynamics
   \consists "Axis_group_engraver"
   \override VerticalAxisGroup.staff-affinity = #CENTER
   \override VerticalAxisGroup.nonstaff-relatedstaff-spacing =
     #'((basic-distance . 2) (minimum-distance . 1) (padding . 0.5) 
(stretchability . 1))
   \consists "Dynamic_engraver"
   \consists "Multi_measure_rest_engraver"
   \hide MultiMeasureRest
   \override MultiMeasureRestNumber.direction = #DOWN
   \override MultiMeasureRestNumber.Y-offset = -1
 }

 \context {
   \StaffGroup
   \name CustomStaffGroup
   \alias StaffGroup
   \inherit-acceptability CustomStaffGroup StaffGroup
   systemStartDelimiterHierarchy = #'(SystemStartBrace a b)
 }

}

% Begin Score Output
theGroup = \new CustomStaffGroup <<
   \new customStaffUp = "up" \relative c'' {
     \clef treble \key a \major \time 6/8
     \repeat unfold 2 { r8 r8 <e e'> r8 r8 <e e'> | }
     R2.*2 |
     \repeat unfold 2 { r8 r8 <e e'> r8 r8 <e e'> | }
     \break
     \repeat unfold 2 { r8 r8 <e e'> r8 r8 <e e'> | }
     R2.*2 |
     \repeat unfold 2 { r8 r8 <e e'> r8 r8 <e e'> | }
   }
   \new PianoMMR {
     \repeat unfold 2 {
       s2.*2 | \compressMMRests { R2.*2 } | s8 s8 s8\ff s4. | s2.
     }
   }
   \new customStaffDown = "down" \relative c {
     \clef bass \key a \major \time 6/8
     \repeat unfold 2 {
       r8 r8 <e e'> r8 r8 <e e'> |
     }
     R2.*2 |
     \repeat unfold 2 {
       r8 r8 <e e'> r8 r8 <e e'> |
     }
     \break
     \repeat unfold 2 {
       r8 r8 <e e'> r8 r8 <e e'> |
     }
     R2.*2 |
     \repeat unfold 2 {
       r8 r8 e r8 r8 e |
     }
   }
 >>

\score {
  \theGroup
  \layout {
    \context {
      \CustomStaffGroup
      \override VerticalAxisGroup.staff-staff-spacing.padding = #4
    }
  }
}

\markup \vspace #10

\score {
  \theGroup
  \layout {
    \context {
      \CustomStaffGroup
      \override VerticalAxisGroup.staff-staff-spacing.padding = #14
    }
  }
}

\version "2.24.4"
%%%  SNIPPET ENDS

Cheers,
Kieren.
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