Your Para 2 or your reps (conflation of payment and appeal time periods is now pretty much a dead duck, and adjudicators won't cancel a PCN on it. This is probably because the Act under which the PCN is issued is flawed, as it defines a two different periods, one for payment and one for representations.
Your first point can win, but it's not a slam-dunk appeal, but see what the "terriers" on here say. They may be short of rats to chase at the moment !