Take a roller and roll your soon to be lawn. That will imbed the seed into the dirt somewhat. A lot of people don't even put straw down, but it realy helps to keep the moisture in so the seed will germinate and grow.
If it were me, I would probably get some more straw, spread it out even if you have to do it by hand, then water things in. Once the grass starts to come up through, don't rake out the straw, but mow everything and chop the straw up along with the grass. Just go in opposite directions so you get an even covering. If you have a rider, raise the deck up to evenly distribute everything. After about three or four mowings and the grass toughens up some, then you can give it a light raking to get rid of some of the excess . But don't rake hard as you'll pull the grass up as the roots will still be small and tender.
I just bought a 50lb bag of more seed and I'm going to take your advice. I'm going to lay this all down and work it in as best I can. It's about half an acre so I doubt I have time to roll the whole area! I like the mow idea though and I certainly won't rake it and jerk it out by the roots. Thanks!

