... drop to zero and flip the sign, significantly before the scale reaches
zero (i.e. before Big Bang)?
That would mean not more and not less than that there was no Big Bang singularity. The universe could have started with a volume which was small but not zero. As we are not able yet to apply physical laws to the very first period of the universe, both possibilities cannot be excluded (pointlike singularity or very small volume).
Is this initial deceleration a generic feature of such an model, or is
it present in those graphs for no particular reason and can be
What you are calling initial deceleration is due to the triple energy in the universe: radiation, matter and dark energy. In the beginning the universe was dominated by radiation and matter. Dark energy is proportional to the volume of the universe and has an extremely low energy density.
After the Big Bang, radiation and matter lost more and more of their pressure and the space expansion slowed down. This exactly is the initial deceleration of the universe. But as space expanded, dark energy became more and more dominant. We presume that 4 billion years after the Big Bang the universe became dark energy dominated. In contrast to radiation and matter, dark energy is proportional to the expanding volume, and its pressure is increasing and accelerating the expansion of the universe.