Here is my suggestion but, will take a sunny day and all day to do it.

In the morning take some spray paint and not the shade and full sun areas.

Same a mid day.

Same in the afternoon.

The areas that get the most shade and are might get the most moisture with ladino clover. The full sun area use red top clover.

You will have to take a leave rake and remove the leaves you can hand seed the clover. But sure you use inoculent(sp) I mix my with a can a coke the day before. It is a little late in the year for clover. But should come up later in the season.

You can take a hand sower to sow it and also take a small tree top and draw it over the area to cover the see a little.

Milo is a hardy plant that might work also. Sunflower take the heat well might try some of them.

But if all else falls short. Try to plant turnips in August typically you have to have loose ground. But the see is cheep and does not take much.