Tom I believe that you have identified the issue above. From experience I wouldn't solely rely upon the Police as it cannot be proved. I would log the complaint with the police as a record and then leave car parked in the same location with surveillance. Using your car as bait doesn't sound wise although you have to catch the geezer in the act; it sounds like he has a real issue therefore it probably wont take long for a repeat performance.
I returned late from a night out with the GF about two years ago and parked in front of a neighbours house minutes before they appeared (looking for a space). Parking is a nightmare where I live, its a terraced street with no ownership over parking spaces....its a lottery. I returned to my GF's Mini the next morning to find that it had been keyed across three panels. We tried everything to prove that it was them, politely confronted them asking if they had seen anything as they were around at the same time (recorded this via a phone in the pocket). Requested for information from other neighbours. My GF even works for the local Constabulary. We reported it, they were taken to the station and questioned but nothing could be proved.
Still to this day I frequently cross paths with who I am 99% sure did it. I feel like they know I know they did it, but it cant be proved. SO many people have stated that 'revenge is a dish best served cold' and I'd be lying by saying that I haven't considered keying their car across the same three panels to enable them to appreciate the cost implications. But is it really worth it, what would I achieve? Do I want to tarnish myself with the same brush as them - no. My father runs a garage so we drove home two of his loan cars (an old rusty Merc and focus) and left them outside of their house for months. Slightly satisfying by didn't enable us to recoup money.
Try and catch him in the act or call his bluff. IMO you dont want to alert him before catching him in the act.