Best solution? Ankhegs!
Genetically-engineered Ankheg's of course. Genetically remove their ability to synthesize Lysine, so you have to supplement their diets with it. Then, once the gerbils are all gone, just stop supplying them with Lysine and they'll die off as well.
Heck, it worked in Jurassic Park, right? I never finished the book, but everything seemed to be going well.