I am really sorry to hear that you have ended up in this situation. It sounds like you didn't realise the RC hard expired and in a panic did something silly in altering the date. Just wait for the letter to arrive in the post. They are highly likely to accept an out of court settlement if you request this given it is your first time offence.
It does strike me of people will openly admit to doing somthing wrong. Personally, I'd say nothing if I got caught (you do not have to say anything). I would only ever provide my name and address ONLY and this would be when I'd done something wrong. Remember too you do not have to wait around for railway staff to confirm any of the details you've provided is correct (although hard to do on a train) and NEVER EVER sign anything. Why help someone try to bring trouble on you.
That is absolutely great advice. Well, only great if you want to end your journey in the company of the BTP with far far bigger problems than a relatively minor ticketing offence.
As to our OP friend you really have left your soft underbelly exposed here. I would not be surprised to see an out of court offer rejected. Thinking about this from the point of view of EMT you didn't decide to give yourself a day extra or a week, you tried to alter it to a year extra. But I'm sure we can all agree this will most likely be a RoRA issue.