IMO, don't submit this polemic unless you're prepared to face whatever consequences might follow. You have no first-hand knowledge of this 'scummy firm'.
All you're doing is engaging with extra-procedural channels and ignoring the procedural ones, not that you'd get far with these IMO.
You have identified the driver in this thread;
If any part of a defence relies upon the display of a valid Blue Badge then, as this is yours, if presented as evidence in court would likely identify the driver.
None the less, how can you give yourself the best chance here, whether successful or not?
I suggest you go back to the start.
At the time, [the driver] believed the signage indicated that Blue Badge holders did not need to pay. However, .. Wise Parking [have since been contacted] and [they] informed that Blue Badge holders are required to register at the reception—something [the driver] was unaware of and therefore did not do.
It took quite a while to find a parking space, and in the process, there was a delay between reading the signage and actually parking. Given the time and frustration involved, it’s possible [the driver] misinterpreted the instructions.