Words I got from a guy was that you could take a swing at a tallow with a machete and spray some 2D4 in it and be good to go,, from what you're saying that might not be the case.
It's called frill treatment or girdle treatment.
A 6" diameter (or larger) tallow tree takes more than one cut. I try for at least 3 different slashes around the tree. One cut will result in the foliage on that side of the tree dying, while the rest of the tree and it's root system continues to grow.
If you have lots of big trees, and you have the time to do so before dozing, I recommend you frill treat the big seed makers about 1 month (or more) before dozing the trees down. Probably not what you want to hear, and it may not be necessary if your dozer operator has a good root-rake for his machine. No matter tho, the seeds are long lived in the soil (years) and the tallow will be an ongoing fight for a long long time.
But, you are miles ahead if you can at least get rid of any tree mature enough to produce seeds.
Your nearest information asset is going to be McNeese University. Outside my range and state of course but I have read lots of good articles and in-field work they've done on S La invasives and agriculture in general.
Do lots of research--there are plenty of websites regarding tallow trees.
I'm going to try some Imazamox on them later in the year. It was originally an aquatic plant herbicide but Fla and La have had good luck with it on tallow trees.
