The crows are doing our work for us. The method might be messy, but cane toads should be exterminated in non-native habitats as expediently as possible.
Instead of feeling bad for them, why don't you feel bad about the species they have almost wiped out?
At some point you have to decide what your priorities are and start culling. E.g. Australia wants to kill 2 million feral cats over a decade, as there are 30 million of them, and each one kills 3-20 native animals a day. [0] At some point you have to make decisions and decide which is more important. If you could teach crows how to eat cats, Australia would like to have a word.
[0] https://news.vice.com/article/feline-massacre-australia-unve...