So I core aerated and overseeded my lawn two weeks ago. 90% of the lawn looks great and germination has not been an issue. But in the back lawn which was completely overrun with crab grass this year, has a bunch of areas like the one pictured. You can see that where the seed made it into the aeration holes, the grass is growing. But the seed has no chance in the other areas. Going to attack these areas this weekend before it is too late in the season.

My plan is to dethatch using my mower attachment and then dethatch again using the rake. Then put down some loam and then seed. Is this the right way to do it or should I be exploring other options?

Any advice would be greatly appreciated.