I am pretty confused as to what your position is at the moment. So in your opinion you have paid whichever organisation the £3.20 you think you owe, and you consider that you have done everything right. Is that a fair summary?
Ignoring all the other side-discussions, if that were indeed the case, then surely you have nothing to fear. You can very confidently allow them to take you to court, should they decide to do that, and after presenting your side of the arguments, you believe the judge will find in your favour. From what I can see, a large number of posters also appear to agree with you.
So in essence, nothing else needs to be done from your part, apart from preparing a pack for the court for when/if needed. You can confidently get on with life and ignore all future communication from whoever, until the day of the hearing.
I am not as confident as some other posters, but largely because I am not sure where you stand legally, but if it were indeed so clear-cut as some others have suggested, there is no more you need to do except what I outlined above.
I cannot see myself agreeing with it, for the simple fact that there is no guarantee you will definitely win should it go to court, and by your actions trying to sort it all out, I get the impression that you are not 100% sure either. All of the above would have only made sense had you been absolutely confident that you were correct, but if that were the case, there surely would be no need to have any further involvement with either SET and IPFAS. In the event that you are taken to court, you can grab them by their goolies comprehensively.
All of this means that it would have made much more sense to have simply sent £3.20 to the registered address or relevant personnel as DaveNewcastle pointed out, or, since you requested assistance from Transport Focus, to have followed what they agreed with SouthEastern. I find it unfortunate that you did neither.
Obviously I wish you luck in your endeavours, and am sure this will be resolved one way or another, but I have big questions over whether all this hassle for the effort you invested in it is all worth it. That, I suspect, only you can answer. I hope that expands on my post four upthread, and explains my take on this whole matter.
I don't think the OP wants to go to court. They have, of course, done nothing wrong, but the OP seems quite worried about the threat of court action so to suggest the OP is confident that they can have their day in court seems a little unfair.
Regarding simply sending a cheque with a covering letter to a nameless financial director based at the company's registered address in Newcastle: I remain sceptical that this would have resolved the matter in the quick and resolute way some would have us believe. Perhaps it would have? But it is equally (if not more) likely that the nameless financial director, who has many more important things to worry about, would have simply passed the information down to the customer service team to deal with, which I fear only would have exacerbated and delayed matters further. I further suspect that had the OP followed this advice they would still find themselves chastised by some quarters on here. Whether or not payment should have been sent to the nameless financial director is moot - the OP actively sought clarification about who to send payment to, was given an answer (which may or may not have been correct, but was nevertheless accepted as correct as any reasonable person would have done) and duly paid the body they were led to believe they should. So this is not a case of the OP having simply paid whichever organization they think they owe. Such a belief is not self manufactured but based on clear correspondence with the parties involved in the dispute.
Secondly, regarding Transport Focus's offer to pay the penalty on the vague promise of a refund. This was clearly an unsatisfactory offer. The OP's trust in the railway industry had already been significantly eroded by the incorrect imposition of a penalty fare and the failure to cancel it upon what should have been a clear cut successful appeal. I also posed the question further upthread of what the OP's legal position would be had they agreed to pay the penalty, thereby accepting full liability for an offence they did not actually commit; a question which seems to have been overlooked by those who profess to have the legal knowledge. All of this aside it remains the case that the OP has paid who they were led to believe should have been paid. The OP was quite conscientious in clarifying who payment of the fare should be sent to was was given a clear answer.
Given payment has been made I reiterate to the OP that my advice is now to engage in conversation with the relevant parties to determine whether payment has been received and that the matter has been resolved. In this case I would strongly recommend telephoning so you can engage in a conversation.
In all cases, the righteous indignation (which is sometimes direct and sometimes indirect, and which may or may not be intentional) that the OP is somehow at fault in this whole sorry affair must stop. The incontrovertible fact remains that this dispute is wholly of the railway industry's making - it is a shame that the onus and responsibility is being placed on the OP to resolve this matter and not the railway industry.