Hi Gordon,
I've tried to make a 'Cita Previa' on Torrevieja town hall's website for both certificate verification and padron, and received the following message, "All available appointments have been exhausted. Sorry for the inconvenience."
Apologies if this sounds like a silly question, but what makes you think that Punta Prima comes under the municipality of Torrevieja? I believe it comes under Orihuela Costa. That said, I haven't been able to book an appointment at the Playa Flamenca town hall, but I was able to book one at the Orihuela City town hall for 11 November. Another member who lives at Pinar de Campoverde also has a Padron appointment at Orihuela City, as her representative also was unable to make an appointment at Playa Flamenca town hall.
However, as I mentioned previously, Town Halls verify ACCV certificates; if you've obtained the FNMT certificate, you'll need to go to the Tax office instead.
Kind regards,
Kim