Are there other species aside from monarchs (insects or otherwise) that consume milkweed? If so, how do I prevent this from happening, or at the very least limit the amount of competition for milkweed in my yard?

There several species of mammals and insects eat milkweed (see additional post for more details). Milkweed is part of a complex ecosystem that supports many kinds of creatures! Planting large amounts of milkweed will help reduce the competition for milkweed between monarchs and other species as well as any competition for milkweed between monarch larvae. You can also try planting several patches of milkweed in different areas to help distribute the consumption between areas.