If you kill with a herbacide and till the ground then re-seed, be prepared to have several weeks or months of mud for a backyard before you have enough new grass to create a ground cover. SOD is the quick fix but way more expensinve.
Also, if I were seeding this late in the summer I would plan to come back in November/December timeframe and also sew some type of winter grass like rye. This will give you some live grass as ground cover during the winter if you do not have a good spread of the new summer grass you planted previously. Most other lawn grasses go dormant in our winter months... (I'm also in Memphis).
Another option to think about instead of starting from scratch is to get a broad-leaf herbacide and do several sprayings over a few weeks. This should kill everything that is not lawn grass so you can really tell what you have on the yard as far as grass. Just getting all of the broad-leaf plants out will make the grass grow better/faster.
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