Glissando from note A to note B, traversing multiple stems with hidden noteheads

[Mike Solomon]

Hey lilypond users,
    I am trying to write a glissando from note A to note B while traversing
several headless stems and, so far, have only come up with the following
solution: 

headless = #(define-music-function (parser location) ()
#{
    \once \override Staff . NoteHead #'transparent = ##t
#})

\relative c'' {
    c4\glissando \headless b\glissando \headless a\glissando f
}

In this example, the glissandos are disconnected where the transparent
noteheads begin and end.  This is in addition to the larger problem that the
glissando from the headless a to the f has a different slope than the
others, and ideally, I'd like one smooth line from c to f.  I've
experimented with a variety of kludges including raising/lowering noteheads
to interpolate linearly between note A and note B, but this still does not
solve the problem of disjoint glissando lines at the transparent noteheads.
It seems like a simple solution would be allowing for a glissando to connect
to a non-subsequent note, so in the above example, having the glissando
connect from the c to the f and budging the stems of b and a accordingly to
connect with the gliss.  However, I don't know how to do this.  Your help
would be greatly appreciated!

~Mike