Those roots are HARD to kill.
Have you heard of Farmer Managed Natural Regeneration (FMNR) of trees in drylands? Particularly in the Sahel, Africa. From wikipedie
"Existing indigenous vegetation was generally dismissed as 'useless bush', and it was often cleared to make way for exotic species. Exotics were planted in fields containing living and sprouting stumps of indigenous vegetation, the presence of which was barely acknowledged, let alone seen as important.
This was an enormous oversight. In fact, these living tree stumps are so numerous they constitute a vast 'underground forest' just waiting for some care to grow and provide multiple benefits at little or no cost –and each stump can produce between 10 and 30 stems each. During the process of traditional land preparation, farmers saw the stems as weeds and slashed and burnt them before sowing their food crops. The net result was a barren landscape for much of the year with few mature trees remaining. To the casual observer, the land was turning to desert. Most concluded that there were no trees present and that the only way to reverse the problem was through tree planting."
The key point is that after decades of regular cutting the roots were still there, and when the cutting stopped they regrew to full sized trees. And this too in an incredibly hostile arid environment.
Our place has an area of about an acre that grew up to dense saplings of willows within 2 years from when the farmer stopped caring for it. Short of digging the roots out they seem unkillable. I have a stump sprouting from beneath my bonfire spot! Rather than kill them, I have decided to work with them. Some have been left as posts to secure chicken fencing to. Others have been cut to ground level, and allowed to resprout. We beefed up the fencing in the area and now periodically let the sheep in for a week at a time. The browse back the regrowth and are encouraging the transition back to mostly grass, with some canopy.
It sounds like your primary aim with this land is to keep it unforested, for fire prevention purposes. I would, therefore, propose that you follow a similar approach. Get your fencing and water supply up to scratch and make a deal with a local farmer. Our arrangement is that they run their sheep on our land spring and autumn (resting in summer) and they keep our freezer stocked with lamb. Everyone wins. If the land is of a decent size consider making two separate subdivisions so that the sheep can graze one area intensively, before being switched back to the other. With sheep in place doing most of the hard work for you, all you will need to do is periodically come through and hand prune any that got too big for them to handle.