For me, focus is all or nothing during work hours. I'd much rather bring fire for fewer hours each day, and then recharge with some of my other pursuits.
This is the first time in more then a decade that I am working in such a regime and I'm not really convinced that I am now more productive then ever. Au contraire, I have the feeling that I'm working more on autopilot and I'm a lot less creative in solving problems.
In the past when I was dealing with a problem, solutions often came when I was doing something mundane like driving or gardening. I got my best solutions/idea's when I was away from my computer. The moment you could switch off and put your unconscious mind to work, now I frankly don't have the time.
But I find I can only keep my knowledge current and skills sharp by putting in a lot of time.
If I worked half as much, I'd be worth less per hour, and total income would drop far more than 50%.
Not sure if it would pay enough where you are; and not sure if you would want to try it (not easy work if you do it properly).
Teaching can be fractionalised quite easily - I do 3/4 of a standard teaching week so I teach fewer classes spread over 4 days. To fit your second paragraph, you would need to be very disciplined about getting the preparation and marking done within your chosen working days.