Why are you concerned about which way you turn them? When I turn them I may go left, I may got right, I may go end over end. I can't imagine a broody hen always turning them back and forth like that.
When I incubate I use an automatic turner that tilts them 45 degrees to the left then 45 degrees to the right of a full 90 degree turn several times a day with the pointy end down.
Now that my wife has a house dog I don't trust, I no longer use the auto-turner when I store them for incubation. I mark one side red and one side black and go a full 180 degrees each time. Whether you use x-o's, numbers, or colors doesn't matter but it helps me a lot to mark them so I know what I'm doing.
That turning schedule should work fine. What you want is for them to spend about half their time one way and half the other. Most of us have top work out a hand turning schedule that matched our life. Most will have long stretches where they can't turn them, at school or work or when sleeping. Spread them out as much as you reasonably can but a lot of people use an odd number of turns each day. If your long stretch is when you are asleep then with an odd number of turns you alternate which side is up at night.
There are two main reasons you turn them during incubation. Turning helps body parts form in the right places. Turning also helps stop the yolk and developing chick from touching the inside of the egg shell and getting stuck. After a couple of weeks the body parts have formed and a membrane has developed around the chick to prevent it from sticking to the inside of the shell. After two weeks you don't have to worry about turning them, but most people do. If you use an automatic turner turning isn't a problem and it's convenient to remove the turner as part of going into lockdown.
