Beth Rags,

Assuming you're in the U.S., have you tried your local Victims Advocate? You can report a crime - the theft of your expensive doormat, and then see if you can get reimbursed (at least partially) from the jurisdiction you're in. This will also help support the data reporting for crime victims, and to demonstrate how property crime affects victims. They will help you when the non-emergency line (either 211 or 311 in your area) doesn't help you.

Here's some information about victim advocacy:

National Center for Victims of Crime

Victim Support Services

Aftermath