Roundups, sterilization and long-term holding are effects. They are outcomes of a process. If you want to change the outcomes, you have to look upstream in the process.
Why are these effects occurring?
How much forage has been allocated to public-lands ranchers? How many horses would it support? What is the true AML? How does the current herd size compare to that? Would the roundup be necessary if the HMA was managed principally for wild horses?
Why is it managed primarily for livestock? How are resource allocations determined?
Why are the horses treated like pests on land set aside for them?