In my opinion, I would back fill with a good Sandy Loam Soil. Sand will fill in better and can be compacted better. I would add this loam and then water in and then add more. You will notice that before you water the soil will look good enough, then after watering it will melt way down.
Grass's will nicely grow in this soil.
how much you will need depends on seeing the areas. You can use this stuff anywhere and in Texas, its more economical to get buy 5 yards and be done with it.