Hi Lshep. You will probably find that the change over days are more flexible out of the main season. Most owners do try to keep to a particular change over day throughout the season for two main reasons. The first being that to be flexible could cost rental weeks. Most people like to visit for a week or 2 weeks. To change days can cut into the weeks available. The other reason is down to the availability of cleaning staff. During the high season obviously the cleaning companies are extremely busy and most like to plan their work load in advance. It can be quite a challenge for the cleaners in the height of the season. You will note also that you are required to enter and leave a property by a specific time. This is to allow cleaners access. They know they have that window of time to do their job.
With our villa, we run Saturday to Saturday through out the main season but are flexible at other times, including the length of time someone may wish to stay.
Just a suggestion - if flights are so much more expensive on a Saturday I wonder if you have considered a Thursday as an example and staying somewhere else such as Palma for a couple of nights? Alpha rooms are very good for finding cheap rooms for a night or so and you get to see somewhere else. Anyway it is your holiday and that was just a thought.
Keep trying by contacting the owners directly. Good luck.