Dave, what kind of soil do you have? (to others - DFW is a soil transition zone, and there are several distinct types in the metro area). I'm now in the cross timbers, but until 2013 I was in the black gumbo.
I have lots of kinds of improved elaeagnus - autumn olive, goumi, silverberry, etc. These grow well, but don't fruit well as understory (for me). I highly recommend "hybrid silverberry". I ordered mine from One Green World, but I do rarely see (smell!) them growing around DFW. They smell heavenly when they bloom in Nov/Dec, and are one of the rare bee foods blooming at that time. I guess you could chop it, but I just prune slightly as a specimen. It is in the sun, but right next to an nectarine tree.
One of my most prolific mulch understory plants are the bird-planted Cherry Laurel (aka Laurel Cherry)
trees. These are evergreen, beautiful year round, birds love them,
bees will eat the blooms, and you can probably cut them every two weeks. The leaves are waxy and don't break down quickly as mulch. The neighbors think they are weeds.
I let the mimosa stay now, mostly to atone for the sins of my youth trying to eradicate them. The blooms are good bee food and herbal medicine. However, small ones (understory) recover from cutting very slowly. In a large, sunny area, if you let it get huge and multi-year established, then it can work. I have two in the front that I pollard back to 4' stumps about twice a year, and I get a lot of 10-15' woody/leafy switches that I carry to the back. The neighbors say they are weeds and damage your foundation.
For ground cover, I let the
lawn weeds grow wild in spring and fall, but they refuse to grow in the summer: chickweed, henbit, yarrow, narrow leaf plantain,
wood violets, etc. Also Lemon Balm (Melissa) is exuberant and seems to improve the soil. If you can get clover to establish, then it will mix with those--I can only get patches in places they choose for themselves.
Russian comfrey does great for me, if I irrigate it. If you are growing other things that require irrigation, then the comfrey is a great indicator of when to water. When it is wilted flat, you water everything deeply and watch it recover. If you don't want to irrigate, then I've only seen (other people have) success with wood chips.
Lots of things don't grow as well here as expected--I may have persistent herbicides or something. If I think of anything else, I'll post again.
Please let us know what you try and how it works out!