I'd cut the grass very short, rake with a stiff rake, seed it than water regularly. A little more soil added first might help improve germination but some seeds probably will germinate with or without it. JUst don't mow again or you'll mow off your new seedlings. Not sure what you have in mind for future years with that bed, but if you have a good mix of perennials and self-planting annuals it would help. Be sure to include some wildflowers that reseed in your area easily. (For me that would include poppies, nicotiana, nasturtium, petunia, etc), as well as some perennials and the area could become self sustaining. Maybe add some herb seeds too. Many online seed sites sell regional wildflower mixes that you could mix with what you already have. Even Walmart has large, cheap packs of wildflowers that you could mix in. I'd be sure to include poppies, larkspur, and cornflowers! Karen

Not trying to get into the wintersow vs. not wintersow debate here but....... The only time it makes sense to wintersow is when you are sowing seeds needing cold stratification and I know some of the ones you listed do not need it. I sowed the Asceplsis incarnata in early August and plan to put them in the ground under mulch all winter. I am winter sowing some native shrub seeds needing a couple months of cold strat. in pots outdoors and three others that are perennials that specifically need it. There are no hard fast rules to this. To each his own. I rather enjoy sowing indoors in winter and have had very good results and it gives me an uplift in winter to do that. I have had good head starts on healthy plants this way and have sowed many SW shrubs, perennials, ornamental grasses, cactus, etc. I always have something indoors in winter I am sowing. I usually start them in October or November in a large sunny S. exposure window and grow them very cool in the coldest dark months sort of in a wait pattern, then let them get warm again in late Feb when the sun comes stronger. I use lights sometimes if necessary but usually they just sit there in the cold. I am not a wintersower to the degree popularized to a hobby level of lots of containers with holes, lids etc craze with every seed I get being done that way. I just use regular pots in the shade under the carport for the seeds specifically needing a cold period. For penstemons its good, they come up when its still very cold. Some seeds needing cold I direct sow. Sometimes I experiment and try all different ways to see what does best with a backup supply to resow in spring. Look up your different varieties and see what they need and go from there. I have sowed seeds as early as October and had established plugs to put into the ground come spring. Other times I put the late summer sown seedlings in the ground in late fall and cover them with leaf mulch and had good well rooted starts that way in spring. Look at nature, she does that all the time with seeds that have fallen. Mostly, make it fun for yourself and do what you want. Save extra seeds for insurance, or try multiple ways and experiment. Do a test in a damp paper towel with a few seeds to see if they sprout in a few days. Often that will tell you want you need to know.

Iron weed and NE aster will grow in just about any clay soil, they don't need standing water. Seeding rates, by weight, depend upon the size and weight of the individual plant seeds. As froggy mentioned, 1/4 ounce of culvers root is going to be thousands of plants. Compared to a 1/4 ounce of solomens seal, which may only be fifty or a hundred plants. The ratio of grasses to flowers depend upon your goal. I'd probably heavy up on the flowers for a small area. Its nice to have a lot of flowers in a large area, but at some point it becomes cost prohibitive.

The best time to direct sow warm season grasses such as blue grama is spring. You can sow a warm season grass in summer if you are able to keep them well watered and its not too hot where you are. This is a fast growing grass that establishes quickly and easily from seed. it is best to sow the cool season grasses in fall. The Prairie dropseed needs cold stratification and is very slow going from seed. Its best to purchase plants unless you want to wait a few years for mature plants. Santa Rosa Gardens sells plugs for very reasonable, especially if you wait for their spring or fall clearance sales, although they seem to be out of it currently. Big bluestem is another one that takes quite a while to establish from seed as it spends the first year or two putting down deep roots. You didn't mention one of the most beautiful and best warm season prairie grasses of all. Sideoats Grama. It is fairly fast to establish and forms seedheads rather early so its gorgeous all summer, fall and winter. Pictures do not do it justice, a mature plant is very stiff, impressive and upright and it can get quite large. The seeds germinate in early spring and it establishes fairly fast. Another good one that adds hazy purple color contrast and light effects is purple three awn grass. Its a fine bladed cool season grass that blooms purple fading to beige all spring through summer. Comes up very easily and grows fast.