Hi Paul, et al,
Boy its been a long time sense I heard the name Boyd, Texas...
I think your "shovel party" is probably your best bet, mixed with a small tractor and bucket with chainsaws...then compost them. This is your fastest "permie" solution short of eating and other organic uses. This can be a real challenge to deal with, yet manageable, if you can combine bringing back the native grass and not allowing grazing there for a few years. After that then only rotational lite grazing.
There is another "permaculture" solution, yet more involved, and not sure you would be allowed to do it without assistance (which is silly sense it works, and they are native.) That would be Javelina (Pecari tajacu) which love...."They feed primarily on cacti (particularly prickly pear)...." Now I can't say where, or who, but can share that they "farm well" in my opinion, and the meat is very tasty, with great leather for gloves and other leather craft. I imagine that within the year of being on a 10 acre paddock a breeding family of these little guys would clean the place up nicely and in a more environmentally sound fashion. The places I have seen this done was in AZ but "under cover" as this is a protected species (even though there is a hunting season.) Wild orphan young were raised over a few years and then placed in the paddock. They now have over 30 head on about a 10 acre paddock the last time I was there in the late 1990's.
This could be a solution and a side business as well if you are "game" for it. I know Boyd, as I had to deliver some "retired" big cats from Florida there in the 80's to the
International Exotic Animal Sanctuary. They, or one of the other "game parks," may tell you how to go about getting the licences to do this. "Peccies" are native to West Texas and there is a hunting season there as well...so good old governmental "Fish and Wildlife," would have something to say I am sure. I grew up hunting, eating and tanning there hids and have raise a number of "pecclets," as my Grandmother would call them. Great animals if you get to know them and not the "horrid creatures" so many claim them to be.
Good luck,
j