Custom DrumStaff

[Cynthia Karl]

I'm trying to duplicate the behavior shown in the next two images:

(the dash above the eighth rest in the upper line in beat 1 of measure 4 is an 
artifact; ignore it)

My best effort so far is:

\version "2.19.15"

\paper {
  ragged-right = ##t
}
#(define percussion '((lobongo default #t  3)
                                   (hibongo default #t -3)))
upperMusic = \drummode {
  \time 2/4
  \stemUp
  R1*2/4                % 1
  \break
  R1*2*2/4      % 2-3
  r8\p bol8 r8 8        % 4
  R1*2/4                % 5
}

lowerMusic = \drummode {
  \time 2/4
  \overrideTimeSignatureSettings
    2/4 % timeSignatureFraction
     1/4 % baseMomentFraction
     #'(2) % beatStructure
     #'() % beamExceptions
  \stemDown
  boh8\p 8 r8 8         % 1
  8 8 8 8                       % 2
  8 8 8 8                       % 3
  4 r4                  % 4
  R1*2/4                        % 5
}

\new DrumStaff {
  \set DrumStaff.instrumentName = \markup { \center-column { Tri CS} }
  \override DrumStaff.StaffSymbol #'line-positions = #'(3 -3)
  \set DrumStaff.drumStyleTable = #(alist->hash-table percussion)
 <<
     \new DrumVoice  \lowerMusic
     \new DrumVoice \upperMusic
  >>
}

which yields:

DrumStaffExperiment1.pdf
Description: Adobe PDF document

The major things wrong with this output are:
  
        * the rests should be centered on their line, not above it
        * there should be a full-measure rest on the lower line of measure 5
        * the 8th rest in beat 2 of measure 4 of upperMusic has disappeared, 
presumable consumed by the corresponding quarter rest in lower music at that 
time.
        * I get the warning:  30: 5: warning: cannot resolve rest collision: 
rest direction not set
                                 4 
                                        r4                      % 4

Can anyone give me a hint or two?  Is a DrumStaff the wrong approach? ( Maybe a 
couple of RhythmicStaffs would be better?)

Thanks.