Thanks to everyone for your suggestions and support.
Sue - These are not tiny mice but larger rats. They literally stand up on their hind legs and pull the scapes down with their front paws to reach the seed pods (that's my guess). No climbing. When they are hungry they will do whatever they have to, to survive.
Cindy - So sorry to hear you recently lost your cat. I know about having to put down a beloved pet. It's heartbreaking.
Thanks to the rest of you. I hope no one else here ever has to deal with this problem. I gotta say ... if something can happen, it WILL happen to me! I am the queen of challenges ...