Dear Kieren,
I think I've sorted it out.

>
> > On one system, the piano staves are ridiculously far
> > apart. How do you bring them closer together?
>
> Have you looked at the documentation on vertical spacing, particularly
> <http://lilypond.org/doc/v2.12/Documentation/user/lilypond/Explicit-
> staff-and-system-positioning#Explicit-staff-and-system-positioning>
>
> It's relatively easy to control the (explicit) position of a single
> staff.
>
> Hope this helps!
> Kieren.
>
> Thanks for the pointer to the documentation. I extracted the

following code and have put comments in:
%start
\version "2.12.2"
 \score {
    <<
      \new Staff <<
        \new Voice {%Spacer track containing line breaks,
        %system positions and distance between
        %the two staves of each system.
          \overrideProperty #"Score.NonMusicalPaperColumn"
            #'line-break-system-details #'((Y-offset . 20)
                        (alignment-offsets . (0 -10)))
%Line-break-system etc. gives the position of the first system on the page.
      %Increase the Y-offset number to move the system down.
      %Alignment-offsets etc. gives the distance
    %between the first two staves: -10 is narrower than -15
          s1*5 \break
          \overrideProperty #"Score.NonMusicalPaperColumn"
            #'line-break-system-details #'((Y-offset . 60)
                                           (alignment-offsets . (0 -15)))
%Line-break-system etc. gives the position of the second system on the page.
      %Increase the Y-offset number to move the system down
    %alignment-offsets etc. gives the distance
    %between the staves: -10 is narrower than -15
          s1*5 \break
          \overrideProperty #"Score.NonMusicalPaperColumn"
            #'line-break-system-details #'((Y-offset . 100)
                                           (alignment-offsets . (0 -15)))
%Line-break-system etc. gives the position of the second system on the page.
      %Increase the Y-offset number to move the system down
    %alignment-offsets etc. gives the distance
    %between the staves: -10 is narrower than -15
          s1*5 \break
        }
        \new Voice { \repeat unfold 15 { c'4 c' c' c' } }%The top stave.
            %Repeat unfold 15 gives 15 bars of music.
      >>
      \new Staff {
        \repeat unfold 15 { d'4 d' d' d' }%The bottom stave
      }
    >>
  }
 %end
This produces a useful demonstration.
In my particular case, there are four voice parts with lyrics
and a piano part, so I ended up with:

\overrideProperty #"Score.NonMusicalPaperColumn"
            #'line-break-system-details #'((Y-offset . 70)
                        (alignment-offsets . (0 -7 -14 -21 -28 -35 -42 -49
-59 -70)))

which may need a bit more adjusting but is very satisfactory so far.
I wasted time because I failed to notice that the lyrics count as a
staff. All I had to do was insert the \overrideProperty
etc....(alignment-etc.
immediately after a \break and put a \break at the end of the system.
The Y-offset etc. is the position of the system on the page,
and the alignment-offsets numbers etc. are the position of each stave and
line
of lyrics within this system. With a bit of juggling, Bob's your uncle!
Thank you once again.
Yours, Fred.
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