I like your method ok. Many things difficult to tell without a photo or more info. I would add the power rake or slit seeder step others recommended to all the steps you listed. Also, I would bring in 1.5 yards of compost and distribute it as evenly as possible after you seed. That is only enough material for approximately 1/8" 'layer' so you will not be changing the elevation much. Drag it or lightly rake with upside down leaf rake to bed the seed. Just walk back and forth with upside down rake trailing behind you. This is a relatively small and manageable area. It is late in the year, it is going to need some water everyday that it does not rain for 3-4 weeks after you drop seed - a few minutes just to keep surface damp.
In terms of price per hour, that has to be your call. These kinds of jobs always take more time than it seems in prder to do it well. You're looking at 35-40# of seed, about 2 hours total of running around getting things and returning others, Around an hour each with aerator and power rake, 20 minutes to seed, around 90 minutes to topdress, 30-45 minutes to put straw down, maybe 45 minutes to clean up the site and move stuff out. If it was me, I would figure 2-3 hours total to check on progress over the next 3-4 weeks. Your mileage may vary.