Dear Lilypond users

Am trying to create a hammer-on and pull-off exercise for the ukulele.
I've been able to figure out how to add text markups inside slurs (Lilypond
doco)<http://lilypond.org/doc/v2.12/input/lsr/lilypond-snippets/Tweaks-and-overrides#Changing-properties-for-individual-grobs>and
analysis
brackets (Lilypond
doco)<http://lilypond.org/doc/v2.12/Documentation/user/lilypond/Outside-the-staff#Analysis-brackets>
.
What I would like to do is move the analysis brackets down so they appear
below the slur text.  The order underneath the staff ideally should be slur,
H/P, analysis bracket then string name.

How would I go about doing this?
Thanks in advance.

Kind regards,
Scott Rippon.

% LilyPond version
\version "2.12.3"

\layout{
  \context{
    \Voice
    \consists "Horizontal_bracket_engraver"
  }
}

\book{
  \header{
    title = "EXERCISES"
    subtitle = "Based on AMEB CPM Guitar Step 1 Advancing"
    instrument = "Ukulele G-C-E-A"
    composer = "Scott Rippon"
  }

  % Hammer-Ons and Pull-Offs (Ligados)
  \score {
    \relative c'
    {
      \key e \minor
      \time 4/4
      \tempo 4 = 92
      e8-0-"E"-\markup \override #'(baseline-skip . 1)
        {\halign #-1 \center-column {"H"}}\startGroup([ g-3\stopGroup])
      a-0-"A"-\markup \override #'(baseline-skip . 1)
        {\halign #-1 \center-column {"H"}}\startGroup([ b-2])
      d-1-\markup \override #'(baseline-skip . 1)
        {\halign #-1 \center-column {"H"}}([ e-3])
      e-3-\markup \override #'(baseline-skip . 1)
        {\halign #-1 \center-column {"P"}}([ d-1])
      b-2-\markup \override #'(baseline-skip . 1)
        {\halign #-1 \center-column {"P"}}([ a-0\stopGroup])
      g-3-\markup \override #'(baseline-skip . 1)
        {\halign #-1 \center-column {"P"}}-"E"\startGroup([ e-0\stopGroup])
      \bar "|."
    }
    \header {
      piece = "Hammer-Ons and Pull-Offs (Ligados)"
    }
  }

  \new StaffGroup <<
    \relative c'
    \new Staff {
      \key e \minor
      e8([ g]) a([ b])
      d([ e]) e([ d])
      b([ a]) g([ e])
      \bar "|."
    }
    \relative c'
    \new  TabStaff {
      \key e \minor
      \set TabStaff.stringTunings = #'(+9 +4 0 +7)
      e8([-\markup {\halign #-2 \center-column {"H"}} g])
      a([-\markup {\halign #-2 \center-column {"H"}} b])
      d([-\markup {\halign #-2 \center-column {"H"}} e])
      e([-\markup {\halign #-2 \center-column {"P"}} d])
      b([-\markup {\halign #-2 \center-column {"P"}} a])
      g([-\markup {\halign #-2 \center-column {"P"}} e])
      \bar "|."
    }
  >>
}
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