I think that's the recommended amount.

That is a lot for topdressing. You might want to consider just adding some bagged leaf compost each time you add grains. Frankly, based on your pictures on the regular lawn forum water will do more good in the short term.

1 cu yd per 1000 sq ft amounts to putting down a layer between 1/4 and 1/2 inch (actually .324 inches if I did the math right). I've always seen the recommended rate stated in one of two ways, either between 1/4 and 1/2 inch or 1 cu yd per 1000 sq ft. 1.5 cu yd for 1500 sq ft is the same as 1 cu yd for 1000 sq ft. You could go with 1 cu yd for that, and get a little less than 1/4 inch deep layer (.216 in).

Some things I've read lead me to believe that compost is probably not all that necessary for a lawn if you're using organic fertilizers. According to that line of thinking, the main benefit to the lawn from the compost is the introduction of microbes, but if your soil is healthy, you shouldn't need them. If you're just starting with organics and want to give a "booster shot" of microbes, compost is a way to do that.

bpgreen is correct, 1/4-1/2" thickness is perfect. The main goal is not to smother the existing turf. Once applied keep the area moist (not soaking) for a few days. The "optimal" time to spread the compost would be when rain/cloudy conditions are forecasted for a few days.

Are you referring to homemade compost or bagged?