In reply to Ciro:
The girl on the beach last night told me to park on a spot along the road a bit - off the first corner of the main road in the Porto Christo direction, there's a loop of old road, with a few fig trees in between.
This morning I woke up to the sound of a guy directing parking tourists - he claimed to live with his young family in the house behind the parking area and was taking two euros per vehicle per day. I'm guessing he probably doesn't actually live there, but whatever... he was running around with bin bags picking up the rubbish that ignorant tourists were leaving behind so at least he was providing a service. Didn't ask me for any money, and said it was no problem to sleep here.
A bit noisier for sleeping than down the access road, but when I went down this afternoon, sure enough they'd been round again and issued 200€ fines (100 if paid promptly) to every car on the road... and since that fella's got a decent little earner here, I'd imagine he'll keep anyone breaking into cars away during the day, as the first finger of suspicion would be pointed in his direction.