Please can we see the back of the PCN?
I have checked the traffic order and also the red route designation order for this road and I can't see any obvious problems there, however the council appears to have quite plainly misunderstood your representation.
Nothing you mentioned in your informal representation amounts to a statutory ground of appeal, but you're entitled to have your representations considered by someone who actually understands what you are saying.
It also sounds like you might have some pretty compelling mitigation, though you probably don't want to post the supporting evidence on a public forum. I think it would be worth using evidence of your financial situation for the
strategy of last resort, if that get a failure to consider there is then a procedural impropriety on the basis of which you could appeal to the tribunal.
Don't worry about the discount, as long as the notice to owner is challenged within 14 days of the date of issue the discount will almost certainly be reoffered.
Which leads to the most important question: is the bike registered to you, do you have the V5C, and is the address up to date?