Transposing chords

[John Donovan]

Hi,
As part of a teaching aid, I have the C major scale and the seven main chords 
that I then want to transpose to other keys.
The code I have so far works well, but I'm having difficulty getting Lilypond 
to 
keep the transposed chords in the right range. For instance, in C major the 
first two chords I have are C and F, with the F chord higher than the C. But 
when it is transposed to G major, the G chord is in the right range, but the C 
goes up to the next octave instead of down. I understand this is standard 
Lilypond behaviour, but is there any way of overriding it? I've tried \relative 
commands in various places but to no avail. A minimal example of what I have is 
here:

\version "2.12.3"

thechords = \chordmode {
   c2 f
}

scale = \relative c' {
  \clef treble
  \key c \major
  \time 4/4
  c4 d e f g a b c \chordmode {\thechords} 
}

\score {
    \new Staff {
      \scale
      \transpose c g {\scale}
    }
}

\layout{ }

What I want is the last C chord to be the same as the first. Is this possible? 
I 
did think about writing each chord sequence manually but that sort of defeats 
the point...

-John