That's the part that surprised me - adverse judgements can happen, but unreasonable conduct is very unusual, due to the high bar that you mention. It's hard to see your conduct as meeting that threshold, unless you walked into the courtroom and acted the pillock, which I very much doubt.
County Court decisions can be appealed, if you feel strongly enough, but I personally wouldn't go down that route without professional advice, and there is always the risk that by doing so you throw good money after bad. If you did,
Contestor Legal Services seem to have had some good results in the private parking field (ironically their CEO used to work for BW Legal before turning to the good side), but I don't have any direct experience of them, so don't take this as a personal recommendation!
Sorry we couldn't help you get a positive result on this occasion. One part of the process we can't help with is the judge on the day.