In our area of the world turf grass needs about 1 inch of water per week, providing it is not too hot, too windy, and too dry and then that grass will need more water. The best way to determine how much water your system provides at any one time is to place several straight sided tin cans around and measure how long it takes to deliver that 1 inch of water and run the system that long once a week, or more often if the grass is showing signs of needing more.

When mowing the more of the grass blade you leave, to a point, the better since more grass blade exposed to sunlight helps that grass produce nutrients that feed the roots that grow more grass plants. 3 to 4 inches is a good height. Recycling your clippings right back, mulch mowing, is also good since those grass clippings can supply 1/2 that grasses Nitrogen needs each year and will help provide some of the organic matter your soil will need. How much additional organic matter your soil will need will depend on how much is there. The best thing to use to add organic matter to that soil is compost, but not more than about 1/4 inch each application, much more could smother the existing grass.
Molasses may introduce soil microorganisms but if the soil does not have adequate levels of organic matter they will have little to feed on and if the soil has adequate levels of organic matter the molasses will not be needed.
Many people do go out and buy "topsoil" and most often they get what the seller is selling which, as you found, may not be what you want so you need to know what you want and specify that. Just going to somplace that advertises "topsoil" for sale is like hiring someone to paint your house and they choose the color. You might get what you want but then again you probably will not. We have a landscaper around here that mixes a soil that is about 45 percent sand, 25 percent silt, 25 percent clay, and 5 percent organic matter and if I needed some soil that is what I would buy.

I presume you did all this dirt and seed stuff a few months ago and that is why you are writing now. Spring is a poor time of year to reseed for a couple reasons. Fall is better, so if you are inclined to improve what you are left with in late July, August would be a good time to redo it. I am confident you will be much happier as the effect of mowing higher and proper watering becomes more apparent.

Molasses will improve the population of microbes if you have sufficient real food for them. Molasses only provides sugar. What they need for real food is protein. You get good protein from ground up grains like soybean meal, alfalfa pellets or meal, corn gluten meal, cottonseed meal (but that has other issues), corn meal, or used coffee grounds. The application rate for any of these is 20 pounds per 1,000 square feet. You can apply any day, or every day, of the year without fear of damaging anything. You can find these materials at your local feed store in 50-pound bags. Most broadcast spreaders will allow the small pellets to fall through so you can use your regular fertilizer spreader.

I believe you can get a much better soil test for $20 at Logan Labs in Ohio than you can for $100 at any university. At LL you get a full analysis of micronutrients and organic matter along with the normal NPK and pH type of test. The full micros and organic are extra cost tests at the universities.

Thanks for the replies. So to make sure I am understanding correctly, I should probably put down some type of grain, and then spray with molasses, as this will give them something to feed on and help introduce them into the soil? And will adding grain often help to build up the organic matter, and this raise the soil my sod is growing on (that is primarily my problem,no base)?

Thanks!

Michigan State University Cooperative Extension Service does a very good soil test for $13.00 per sample, and since the lab service is connected with MSU Ag School they have a much better idea of Michigan soil then would a commercial lab in Ohio or anywhere else. The horticultural agent in your counties offiice will also know more about your soil then would someone in a different state.

You said you had a 'clay-based' soil. Before you let the irrigation run for 1 inch per week, you might want to see how well you water is soaking in. Sometimes if the water sits on top w/out soaking in and/or draining adequately, an unhealthy environment is being created for your grass.
You may have to do lesser amounts at a time, until your OM helps the surface absorb more water, more quickly. :

Put down grains alone and you will be so happy in 3 weeks that you will forget all about everything else.