Thanks very much for your comments, Blue Albatross. Andrew Lucas' blog is illuminating.
I mentioned in an earlier post that I'm not intending to actually complete my PPL in 10 days! Rather, that's the kind of timeframe I have available, and I want to get as much of a headstart towards my PPL as possible in that time. So I'm just looking to do as much flying as possible, hopefully at least 20 hours, which would bring me to about half-way through the course. I'll also have studied the groundschool, so I'll arrive ready for the Air Law exam and any others that the school considers a pre-requisite to soloing. I'll then finish the course in my own time at a local flying club in the UK.
I got an email back from AAA yesterday, indicating that they're fully booked for a while (although their PA28 is available). But since it seems that I should allow three months for the visa and TSA bureaucracy, and I'd like to do this soon, I'm starting to conclude that those guys at Jerez might be a better option.