Good job AXPAlum. The police may not accept it as a theft report and your option to recover would be a civil matter, conversion as AXPAlum mentioned. You can ask for things to be put right. I think that you have over valued a 20ga 1100, unless it is a special model. All 1100's are lightly engraved on the receiver. This photo shows the engraving on a standard 1100 20 ga.:
http://www.gunsamerica.com/smpics/976220361-2.jpg
Now if it is engraved with gold inlays (pigeon grade for example) it would be worth substantially more than $800. Used is about $400-$500 for a standard grade 100 try this link:
http://www.gunsamerica.com/search.cg...2251&state=All
This particular shotgun has additional sentimental value to you which means that only THAT shotgun will satisfy you.
Proving ownership will be difficult as I don't believe that Ky has gun registration. You may have filled out a federal 4473 form (yellow sheet) when it was purchased, but that is retained by the selling dealer, never filed with the state or federal govt. The original receipt from when you purchased it and testimony from people who know that the gun is yours and have known it to be in your possession for many years would be helpful to prove ownership.
Hopefully the 'thief' will bring it with him when he returns. Good luck.
One other thing. Remember that you are responsible for the guns you own. If someone where you left the shotgun accessible used it to 'go postal' you have some degree of liability. Remember the girl in Colorado who bought the guns for the murderers at Columbine? Gun ownership has certain responsibilities that go with it. Many states have adopted laws that require a firearm to be safely stored, either in a safe or with a trigger lock. Some of them have automatic minimum sentencing guidelines as well. It is fine to own guns, I encourage it, but please do not make them easily accessible to people who should not have them.