"The voicings are:
Cmaj7 - first inversion
Cmaj - first inversion
Abmaj - second inversion
Fmin - root position"
Ok. So here you have the C at the top of all the chords, which acts as glue - connecting the chords, like a 'pedal point', as Quantum mentions. So, this allows a kind of shifting of tonal reference - from key of C, to Ab major, to F minor ( which, incidentally is the same scale as AbM). You could experiment alternating with other chords as well, with C as the top note. When looking at something like this compositionally, it is a good idea to look at many of the possibilities in this context. You might experiment with Many 'resolution' chords. I mean, you could try for example Dm7b5 (root position), Eb6 (root), DbM7 (root), Gsus (2nd inversion), E aug (root). D#dim. (root) -- and these are just of few... You might try it out just to get a stronger sense of this pedal point idea.
j-tour, If you come across a tune that does this, let us know. Cheers!