So, I'm definitely calling it ID'd as Alligator Weed
(Found a solid ID on a foraging Texas website, but can't share the URL because my account is too young).
As for eating it. I went out and chose mostly young stems, but took some with mature leaves as well. I left the leaves whole and diced up the stems. Sauteed a little spring onion in butter, then in went the greens, sauteed them for a minute, then added some mirin to steam them (didn't have any white wine handy).
They wilt nicely, but don't get soggy like spinach does. Have no discernable flavor other than "green leafy vegetable", and the stems maintain a nice little crunch. Altogether a good, toothsome little side dish.
And bonus - it turns out that using some mirin to finish off your sauteed greens is awesome because it adds some sugar to them. A combo I will certainly remember.
I'm calling this a win all around. As long as your soil is clean and you cook them to reduce the oxalates, it's free greens as far as I'm concerned.
Just imagine, the next time you serve a chicken cordon bleu it can be with a side of creamed alligator weed.