The fact that Leicester half-term starts a week after London is essentially irrelevant to your case, because you would have passed the signs. YOur PCN and the photos shows you passing them quite clearly, so the contravention is made out.  Did you understand what the signs meant ?
GSV shows them closed when the GSV camera van passed in July 2023, so one has to assume that just before the relevant school hoidays, a council official comes along in a van and closes-off the signs.

Your problem is that most of your narrative is an argument based on mitigation, except for the one minute into the restriction.  If you decide to stand your ground and take them to London Tribunals, this could be argued as de minimis, and has won appeals in the past. The tribunal is unable to consider mitigation, so your only appeal would be that one minute.

However, your narrative could warm their stone-cold hearts and get a result, but don't expect one, as London councils have "heard it all before". If they reject your reps, they will, in all likelihood, re-offer the discount. Whilst this is not a legal right, most London councils now do so, provided reps are received within the discount period.They do so to avoid having to prepare an evidence pack for an appeal, which for them is a PITA. This is because, for an appellant, if the discount is not re-offered, it is a no-brainer to take them to adjudication as the penalty remains the same and there are no additional costs.

The relevant document seems to be this: -
https://www.londontribunals.gov.uk/sites/default/files/consolidated-cc-scheme-order.pdf
As far as I can see, none of the current road user charging schemes; congestion, emissions or bridges have a refund process, because when one pays, no date is entered. I suspect nobody has really looked at the revenue arrangements in any detail, except for the 2018 DART case decided by Caroline Sheppard, no less.
Would a council trading standards office be interested ? I have to say I doubt it. Maybe the LGO would take an interest if you get a fob-off from TfL.

The photos won't zoom.
Although website errors can assist with any appeal, there should have been the match date on the signs as you enter the zone; was the date there ?
https://maps.app.goo.gl/x6zLfHJe55FDBXeb9
If the match date was there you haven't much to go on because the law is that the sign is what you must obey. They cannot demand that motorists access their website when turning in or parking.

It seems to me this is the ley sentence: -

Since then a notice to owner (NTO) was served, however due to life events, I was unable to respond within the 28 day period.

Please post your reps that you submitted, albeit late, against the Notice to Owner.

Form TE9 does not seem to cover your circumstances: -
/https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1094509/TE9.pdf

We must see the PCN when you get it, because a 2018 TPT adjudication case involving DART, under the same Road User Charging regulations as Bristol, decided that it is unlawful to demand the toll fee as part of a PCN. It should be noted that Transport for London ULEZ PCNs do not include any unpaid tolls, payment of the PCN concludes the matter. The London ULEZ is under separate regulations, but the content of PCNs definition is the same in both regulations

Yes, I seem to have got this a bit wrong.  With a parking ban at certain times, the bay needs something to indicate that, the sign is not sufficient on its own. Worth a punt at adjudication, I'd say, especially if CP8759 is on the case !

I’ve made my mind up. I am just going to pay it and get this out of my life. I can’t risk it jumping to double the amount. I guess in future I don’t cross the junction until the road ahead is entirely clear and just ignore the honks behind me.

Now you know how councils farm such huge amounts of money from motorists; they know from experience that the motorists (90%+), fold at the first hurdle so always refuse any representation no matter how valid.