Thanks for your replies, both.
I agree with the rather brutal reality of your statement, Incandescent. I don't like it...but, pragmatically, if she accepts that the undelivered PCN was her fault (which it probably was), and if the £279 per-PCN from the OfR still applies, everything afterwards (which arguable was not her fault) hasn't actually increased the size of the penalties appreciably, so there's very little point in railing against it any further.
When she responded to the OfR with a Statutory Declaration, our new address was provided, and that has been used by both TfL and the TEC ever since. Both entities have used the new address correctly previously, but it was incorrectly rendered by the TEC (in two ways, I've just noticed) in their most recent correspondence (i.e. our address on the latest TEC letter is wrong in two places). I think that's probably an irrelevance, though.
Latest letter (with name, address and PCN number redacted) as follows:


My reading of that is that the PE2 has been rejected, which in turn means the PE3 has been rejected, and we're back to square one (i.e. the terms of the OfR). What's not clear is what happens next, and if we need to do anything at this stage, or wait for further correspondence.
Can I come back to the earlier questions? I'm going to assume that the failure of RM to deliver (at least) the CC is not going to get us anywhere (even though it's not actually our fault either!)...but what about the procedure from here, if we conclude that we just want to cough up and draw a line under it? It's far from clear what we do next.
1) Will a further demand be made, or (without them specifying such) should we refer back to the original OfR (which states a figure and how to pay)? It has taken the TEC almost two months to respond, and I'm reluctant to just sit and wait, especially given the record in the case of post going missing. I don't want my first ever visit from a bailiff (or to pay their fees!).
2) Should we contact the TEC (or TfL) for clarification to expedite a resolution?
Even leaving aside the bitter taste in the mouth left by the appeals process (which feels unfair and unjust, to say the least), the clarity over the procedure is exceptionally poor, and I'm left extremely nervous about what might happen next.
cheers
James