How to control Brown Tree Snake populations - Poison filled mice

I came across this article on National Geographic's website and it is about an attempt to control populations of the invasive Brown Tree Snake in Guam. The purpose of this experiment was to control/eradicate populations of the Brown Tree Snake in the U.S. Pacific territory. This invasive species from Australia has been the cause of the extinction or severe depletion of the islands native species. The experimental program  consist of air dropping about 200 dead mice in the jungle canopy. These mice are filled with 80 mg of Acetominophin, though harmless to us, will disrupt the oxygen-carrying ability of the snake's hemoglobin blood proteins. The snake will slowly be induced into a coma and then dies, but it takes nearly 60 hours for the snake to die.

My first reaction was how could they drop all of these poisonous mice into the jungle and not expect other species of snake or any animal for that matter not to eat them as well. They said that the Brown Tree Snake is the only snake species in the Guam jungle that is a scavenger and will eat something that it did not kill. I still feel that there is a possibility that other animals could eat the mice and maybe not die, but have detrimental side effects. I also find it somewhat disturbing that these snakes have to slither around half alive for upwards of two and a half days before they die. This is the second attempt at eradicating these snakes by the USDA and is only one of few different strategies such as snake traps, snake detecting dogs and nighttime spotlight searches. I guess if the attempts have been made in the past then they obviously have researched it and know that the Brown Tree Snake will be the only snake species that will eat the dead mice. I am curious if there would be any objections from wildlife conservation groups or if there are any wildlife policies that would protect the Brown Tree Snake from these attempts at eradication.

Here is the link to the article
http://news.nationalgeographic.com/news/2010/09/100924-science-animals-guam-brown-tree-snakes-mouse-tylenol/