1. Slit the soil. The seeds fall immediately behind slitting blades into the slits/grooves. This will cause the sprouts to be all in a row, "military" style, until they spread and fill in. An alternative is to make two passes, at 45 or 90 degrees, so the rows are less noticable before they fill in.
2. Aerate, then spread the seeds. Some seeds drop into the holes; most remain on the surface. The cores also remain on the surface. At first watering or rain, the cores breakdown and cover the surface seeds. A concern: the aeration holes are over 1.5" deep. So the seeds that fall into them may be too deep. I don't know the long-term impact on a lawn where maybe 10% of the seeds start from a much deeper depth.
Scott's instructions say that for overseeding, it's only necessary to work the top 1/4" in thin and bare areas; for a new lawn they say to loosen the top 2 to 3 inches.
3. Lawndoctor uses their own patented machine, which seems to work like a slitter. But it has many more blades, with smaller spacing between rows, and the slits each blade makes aren't continuous. They sort of stir-up the soil, without damaging existing grass. So there shouldn't be that initial "military" look.
After putting down the seed, none of the companies followup with rolling, to improve seed-soil contact.
Thanks for your comments and recommendations.