I'd be tempted to flesh out that Witness Statement to emphasise some of your points. Apologies, as some of the old links are now dead, I'm relying on memory, but am I correct in thinking the current claim is comprised both of the £70 debt collection charge and the £100 you've already paid?
If so, I'd make this fact far more prominent. Your points around the actual parking event aren't all that important really - no harm in mentioning them, but I'd be tempted not to lead with them, as you're not really disputing the facts of the parking. Instead, your first point should be that you have paid the parking charge - if the core of their claim is £170, then the first £100 clearly isn't owed, as they have already received it, so that and any interest they're claimining on it should not be awarded.
Then, you can move on to dealing with the additional £70, and this being an attempt at double recovery, representing neither costs incurred by contract, or a genuine reflection of the costs incurred in the debt collection process.
