never heard of that method before. Every company that I have talked to stands by not broadcast seeding following aerating. When the seeds fall into those 2 inch deep holes there is no light reaching them which will cause them to not germinate. Seeeds need an adequate amount of water, nutrients, light, and oxygen to sprout. They wont receive the needed amount of light that deep into the soil. Also if you get a heavy rain the water is just going to wash the seed ou of that hole.
First get a good bag of starter fert and apply that to your lawn. Then I would aerate the lawn one way N to S or E to W doesnt matter. Then Take your slit seeder doesnt matter what brand. I prefer the bluebird but either machine will work. Put half the amount of seed you need in the machine so lets say you have a 10k lawn and it calls for 2lbs of seed per k thats 20lbs of seed your going to need. Anyways but 10lbs of seed in there and being to seed in your lawn going opposite of the direction you aerated. So if you went N/S make your first seeding pass at E/W. After you finish that pass fill the seeder up again and this time go at a 45* angle to your last pass so NW/SE and do that.
In looking at the bluebird to the billygoat i like the looks of the billy goat becasue you can convert it to a dethatcher or an overseeder. Two machines in one. looks useful to me. If you wanted to go all out following aerating you could dethatch the lawn then over seed. If you go about that way. Dethatch NW/SE after Aerating then overseed E/W and NE/SW just make sure you slit seed two ways if you dont you will get the cornrow effect.
I have done this to about 5 lawns this fall and had awesome results from it (Aerating/Slit seeding.)