I'm just throwing this out there as I've never tried it but, why couldn't you put a small drip system on your brush hog/mower and apply chemicals down through a hole in the deck?
The blades make a very efficient delivery system.
2,4-D and 2,4,5-T will work when introduced to the vascular system of the woody plants.
I've noticed up here in North Maine that on CRP acres that are mowed every other year the brush tends to come back stronger, but shorter every year so what is actually happening is the bush is reacting to a good pruning.
I've deep plowed a couple hundred acres of this stuff, and the root ball on these "tiny" bushes is huge.
I've also noticed that down in Downeast Maine they clear fields for blueberry production in a similar manner as what you've done and the last eradication step is to have workers with wick applicators wipe the offending plant and they die.
Rope Wick Applicator, Herbicide Wick Applicator, Weed Thief | Agri Supply
From the road, it appeared that they only touch the plant they wanted to kill.
Something to remember is that most ag chemicals are highly corrosive, so a thorough cleaning/rinsing of the mower followed by a good application of oil using the same method as the chemical drip is probably a good idea.
Do it where you don't want anything to grow and get a twofer.