As a college professor, I have never missed class to illness in 16 years of teaching at KU. I have missed for professional travel and once for weather. An excuse to miss class for me, then, would be an illness truly incapacitating or violently contagious, or crashing my car on the morning of class and not arriving. Being too tired, burn-out of this particular class, having a headache, etc... would not be legitimate reasons. I wouldn't miss class because I didn't have time to go, being busy with other things.
So what would it mean to treat your writing time like a class you had to meet? The first thing you will realize here is that the greater flexibility, being able to start writing at 7 or 8 or 9 or 10, is a disadvantage rather than an advantage. It is much easier to treat a class as a fixed obligation because it is at a particular time, and ends at a preordained hour too. Secondly, you will realize that if you miss a writing session, nobody complains! You won't be fired from your job, even if you miss 90% of your appointments with yourself. This, once again, is a disadvantage wrapped in an advantage.
You could probably write when you are even too sick to teach. You can write when you are traveling, as I am doing today in a hotel room. You can write on vacation with a laptop for an hour in the morning and still have a great vacation.
So as an experiment one week, just schedule your writing as you would a class. Six hours a week? Treat that obligation just as seriously. Show up at the appointed time. Have your cellphone and email off, the same way you would while teaching. Lock your office door and pretend not to be there if anyone knocks. Don't worry about not having time to do this. In your new frame of mind that would be like not having time to teach your class.