Here is some poor advise.
The usual is to mow as you say then rake making reasonably good corners, then raking out the mess on the corners. This results in too much dead heading but that is the way we always did it.
If your swather can lay the hay out flat and wide then you can rake to the end, reverse your travel and rake the full length of the field only.
Better yet if your fields are such that you can run a long length and a short cross section.
Figuring the cost per hour to run each piece of equipment, the abler is the highest cost per hour. Save time here save money.
Next is the mower conditioner. Some mower conditionesr can turn and cut back next to the opening swath, but many are not that fortunate.
The least cost per hour to run but the most crucial for good bales is the rake.
Most of my hay fields are 138 feet wide, and are long.