By having to nuke the entire lawn, does this mean that any attempts at
just making a portion of the lawn wild will cause the march of the
non-native grass on the plot of lawn meant for wild grasses and
flowers?

Ah, I thought you were going to be establishing a wild lawn, as opposed
to a small bed. My error. Still, depending on the lawn grasses you have,
you may find your new bed being invaded by your lawn. Bermuda grass,
for example, is oft-cussed by gardeners for its invasive properties.
I've not lived in the gulf coast states, so I don't have direct experience
with what you're growing there, but I've certainly done a fair amount of
weeding on newly established prairie plots. Like anything else, if there's
bare soil, a plant will move into it. The ones that preferentially move
into bare soil are generally termed "weedy".

What are you intending to put in this new bed? Will you actually be
using native plants of Alabama, or are you intending to do one of the
"wildflower in a can" mixtures? The reason I ask is that most of the
"wildflower" mixes are actually loaded with Eurasian species that botanists
would term "weeds" because they aren't native, but naturalized... reproducing
here on their own, and many of them are pretty aggressive seeders compared
to trying to establish native perennial plants from seed.

If you're going the true native plant route, you're probably
in for several years of careful weeding -- fewer if you bring in nursery
stock, more if you do it from seed. I'm not saying this to put you off
the project, but to help you spot some of the potential pitfalls that
many advertisers don't tell you about, so you can figure ways around
them, and accomplish what you're trying to do with minimal outlays of
cash and sweat.

Kay