Have you tried to contact Avalon and see if maybe each Unit has a unique number by which it could be tracked while mining? or something unique to it?

Did you check the pool where you were mining with it, maybe he was stupid enough to test the unit using your credentials/mining address? If he was stupid enough, you could at least get an IP address(from pool) and that would be a start.

I think suggestions like "if someone saw something suspicious in the neighborhood" will not help - the police should be able to take care of that.

I don't know much about avalon but see if there's a way to track it back(maybe avalon developers can help?).

Another thing you could try is inquire every single pool and ask for help by providing the information the day that it was stolen and the week from that day, to see if maybe there was a user which turned on additional 50-60ghs. There might be many of those guys, but by IP you could check and see maybe there's something in your area.

Hope any of this helps.