Specifically, since this is being driven by the development of farmland, does anyone know
1 - Whether eliminating agricultural subsidies would have a noticeable impact, and
2 - How likely that is to happen?
The only cure is a ubiquity of states which are willing and capable of protecting and rewilding these lands, restoring entire indigenous ecosystems, and halting or mitigating the destructive effects of climate change.
In regard to market forces, the US does not subsidize these grazers, unless you mean aid to their host countries.
Our complicity lies in a series of free trade agreements which pushed US production around the world while the carnivorous part of the American diet followed culturally.
As this global demand for meat already exists, the die is cast. It is a problem for culture at this point (short of dietary fascism).
Look at cats and dogs not going extinct. Of course, it's not 'wild animal' friendly.