IMO, I don't think you have a case.
1. The NTO appears to comply with regulatory requirements;
2. The TMO deals with the parking places in Upton as it is required i.e. it specifies that the manner of standing for these parking places
alone is '2 wheels on the footway'; (OK, they've not used the correct traffic sign but instead used 2, one to indicate the parking place and another to indicate 'parking in marked bays'. Councils just can't get this right, but as you weren't in a marked bay anyway, IMO it's academic);
3. You were parked with 2 wheels on the footway where the London-wide prohibition applies;
4. None of the legal exemptions applies, see 15(3) here:
An Act to confer further powers upon the Greater London Council and other authorities; and for other purposes.
5. The DYL and the wrong traffic sign have nothing whatsoever to do with the alleged contravention.
Your optimum outcomes are:
They re-offer the discount, and/or
They mess up their response - another procedural hurdle for them to negotiate.