While the Costa del Sol is still at the head of the list of possibilities, I have expanded my search a bit. My newest area of interest is Malta.
The climate prospects for the winter months in Malta nearly matches that of the Costa del Sol, with possibly a slightly higher probablilty of precipitation.
I have found no facilities similar to the Apartamentos Bajondillo, but there are a number of all-inclusive resorts on Malta that might fit the bill. One in particular offered a room with a sea-view balcony, use of all the resort facilites, all meals, and all beverages, for about $4,500 for two people for 30 days. Malta is small and has a great public bus system. So the entire island is readily accessible from the resort.
Then I looked at air transportation. Oi vey! While Malaga is hard to get to and harder to get home from, Malta is worse on both counts! And the cost of air transportation to Malta is about 25% more than to Malaga. So the month on Malta would cost about $1,000 more than a similar stay on the Costa del Sol, about half of that in air fare costs.
In 2011 we took the Sicily tour with the Malta extension. For our five days on Malta our base was a hotel in St. Julians. Were I to go for a month I would not stay in St. Julians. I would go to one of the beach resorts on the north end of the island. But it is just a half-hour bus ride from Valletta and the "excitement" of that area.
Like I said, I've just started looking at Malta. As I develop more information, I'll add it to this thread.