I can think of at least a few possibilities, and I'm sure more will keep coming to me:
A shows what are, more or less, the actual pitches being sung. But I agree with you that showing these pitches would give the performer the wrong idea.
B then just adds (half spoken) above; this is pretty self-explanatory.
C is in line with modern notation of the Sprechstimme (speaking voice) tradition made famous by Schoenberg. Although it's not exactly Sprechstimme—your example has more pitch—I've put the noteheads on particular pitches to show the general area of the pitch.
And D is another variant of the Sprechstimme tradition (Schoenberg notated it with an x as the note head and as the note stem), but this time I didn't notate any particular pitches.
I'm sure there are other ways than these, but no matter what you choose, I recommend always remembering the fundamental rule of notation: just make clear to your performer what it is you want. Especially in the case of "modern" music, as long as you make your intentions clear, your notation will succeed.