TL;DR version of events:
I received a SJPN. I believe I technically am guilty of the charge, but had ignorantly committed the offence out of sheer financial desperation, having had no money and just started a new job. I'm desperate to avoid a criminal conviction. I contacted TfL's IAP to apologise, explained my circumstances, and I provided proof for everything possible and asked to settle this out of court, and that I'm happy to pay the necessary fine. Today they finally responded - with a very generic response to say they wish to proceed with the case...