I think you have found Veronica peregrina, which goes by the confusing common name of purslane speedwell.

I'm not surprised this one was so hard to run down. It is Diodia dasycephala, which is sometimes called Carretilla, or Clustered Buttonweed. It's a non-native species that has only been found in a few Arkansas and Louisiana counties, to date.

Wow, that was tough to track down! I would have never gotten there. Some of the pictures on the internet do look identical but with species like this we're treading into the recondite corners of the web...

Thanks for teaching me a new word, macranthos.

:-) I find it ironic that the word recondite is not a well known word in its own right. One more new word for you (maybe) is homological: a word that describes itself.