I do a lot of gardening at home and as a 'gardener', I have a pretty good understanding of what it takes to get seeds going. Grass seed will come up extremely well in nothing more than scratched up dirt. But, contact with the dirt (and even a tiny bit of dirt covering the seed) is key. I've got an area I scratched up a few weeks ago where I had thrown seed down and then raked it around so the seeds get covered a little and it's growing like crazy.
What I would do if I had my choice and it was only me doing it is...
1. Mow the grass very short.
2. Rent something to de-thatch the lawn well. I'd de-thatch the crap out of it so the dirt gets scratched up really well.
3. Rent a Lawn Solutions brand seeder and be a little aggressive with it and drop lots of seed. http://lawnsolutionscp.com/Assets/Fi...s-no-crops.pdf
My idea is based on my personal gardening experience knowing that grass seed wants dirt and the best way to give it dirt is dethatching well and then using that nice seeder from lawn solutions to rough up the dirt and drop the seed in. It makes sense to me.