Dear Ben Dribus,
Greetings and thanks for your lucid inquiry.
My answer to your first question is, 1) Quantized acceleration applies only to quantum (or micro) particles and not to classical test masses or bodies. In EVAF, the path described by both quantum particles and classical test masses or bodies is log spiral and it is a continuous path. So the motion of quantum particles and classical test masses can be explained on the basis of 'continuous reference frames' and if 'continuous group transformations' can explain EVAF, then it can be applied. However, for quantum particles the reference frames may be treated as being quantized and accordingly energy transitions can be explained. To this continuous group transformations cannot be applied.
To your second question, my answer is; Quantized acceleration, for quantum particles, is equivalent to quantum of energy but this does n't mean that space-time itself is quantized. It is true that the field equations describe a manifold over the continuum, because the path described is a continuous one.
I have a glimpse of your article and I like your approach towards solving the problems and as soon as I go through it in detail, I surely express my opinions.
Best regards and good luck in the essay competition.
Sreenath B N.