I wonder if any of the genetic control strategies used with the Aedes aegypti mosquito [1] could be used in this case. The obvious difference would be that males would also be harmful to the environment in this case. The strategy could also be improved if actual non-viable offspring was produced, increasing opportunity cost of reproduction and spent energy.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4001467/
[2] https://www.popsci.com/mosquitoes-designed-self-destruct