>"I know I'm forgetting something"

Yes, where do you live to start, LOL!

North Carolina piedmont

There are two approaches to plastic. One is to use black plastic and shade the grass to death. The other is to use clear plastic and steam the grass to death. To use clear plastic you have to hold it down at the edges. Neither approach will earn you any points with your neighbors but they will forget about it when the new yard comes in.

I would not overly stress the lawn. In fact I would treat it like the perfect lawn. I would water it every month until the heat kicks in and then water it no more than once a week. Water it deeply so it lasts until the next week. And if you really have centipede, then mow it low. But if you really have St Augustine (which a lot of people refer to as centipede), then mow it at your mower's highest setting. Healthy grass usually will get rid of weeds by itself. Then next August you can decide if you want to nuke it.

Here's what I would do. First soil tests, now. This will give you time to add nutrients and adjust pH so when the fall comes around your soil will be in great shape to grow grass. When spring comes treat your lawn like you are going to keep whatever you have, adding water, fertilizer, etc. Kill weeds with Weed B Gone or similar product, once in spring, and once in early summer. This will ensure that most of the weed seeds in your soil germinate, and you will kill the weeds early enough so they won't produce more seeds. At this time you should be doing your homework on what grass you are going to plant. I am assuming you will go with TTTF, but whatever you decide, do research on the best cultivar for your area. Study the NTEP trial results, talk to your local extension office, maybe a local university with a turf grass program. Once you decide what you are going to use, find a reputable seeds seller that sells weed free grass seed. Now, it's late summer, I say forget using plastic to kill the grass. It takes a long time, and it produces favorable conditions for fungal growth, stick with Round-up, it works great, it's fast, it's safe, and cheap. You might have to do it twice. Now, once your lawn is dead, and you scalped it there are a few ways to go. Some people like to do nothing, just power rake and plant on top of that. Others like to core aerate, some like to till. Some say don't till, it disturbs the soil too much and will settle unevenly. I think you have to decide what would be best for you. From what I hear NC soil is usually mostly clay and gets fairly compacted. If this is your case I would probably core aerate, break up the cores, and then cover with a good layer of screened topsoil/compost. Then I would roll, seed, roll again, top dress, apply starter fertilzer, and keep moist for the appropriate period of time (there are watering schedules online, probably somewhere on this forum). Also where you live, labor day might be too early to seed. Ideally you want warm days and cooler, less humid nights, especially when you have seedlings. Nights below 60 degrees are important because most harmful fungi don't thrive in this environment. When this weather situation occurs for you is probably variable, but again, do some research. Hope this helps.