hide barline when \startStaff coincides with system break

[mason]

In bar 6 below, where \startStaff coincides with a system break, a lone
barline is drawn at the end of the previous system. I would prefer for
the barline to be omitted in this situation.

In bar 4, where \startStaff does not coincide with a system break, I
have a slight preference to keep the barline.

Is there an override that would cause a lone barline like that at the
end of the system to be omitted? I would prefer that the override keep
the barline before bar 4, but if that's not possible I would accept an
override such that barlines are never drawn at a \startStaff.

%%% begin MWE %%%

\version "2.21.0"

\score {
  <<
    \new Staff \relative c' {
      c4 c c c |
      c4 c c c |
      \stopStaff
      s1
      \startStaff
      c4 c c c |
      \stopStaff
      s1 |
      \startStaff
      \break
      c4 c c c
    }
    \new Staff \relative c' {
      \repeat unfold 6 { c4 c c c }
    }
  >>
}

%%% end MWE %%%

Thanks,

Mason

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