Made it! Somehow. One of the Explore group stands on top of the world, or at least, on top of continental Spain. And yes, that is snow on the left. This is the Sierra Nevada, after all.
These bloglets posted on Thu 19 Jun were originally pictures taken on my mobile phone, and sent from Mulhacén to Flickr and on to here - including this one, from the summit. One more bit of magic! It's now Sat 21 Jun, and I'm back in Salobreña with a broadband connection, so I'm able to edit a bit and add these commentaries - I couldn't see how to do it from the mobile.
There are lots more photos, from my Canon and from the mobile;
I'll also add more to this blog; you'll be able to get to the whole story via this Mulhacén link.