That really sucks, hope you find the prick.
Yeah, I'm sorry to hear that... This is some crazy wild west territory we're in, but this is the first I've heard of someone being physically robbed from to get the coin.
Here's my thoughts based on your information.
1. How many people knew you had this box? They're all suspect IMHO. Including the original shipper... Avalon I presume?
2. Concerning eBay. Who have you done business with in the past that might look at your "items for sale" link that are related to bitcoin. Buy any riser cards? Any bitcoin paraphernalia that would give someone a shipping address on your box based on a previous purchase? All suspect IMHO. I don't see how a random passer by on eBay would be able to obtain your address without buying something or selling something to you.
I also see how anyone would brag about a having a "stolen" Avalon. And if they did, there's honor among thieves... unfortunately.
I hope you catch the bastard! I do!!! I'm sure you've run down all these options... but I'd be looking for people I'd done business with in the past that might be within 0-8 hours drive from where you live. Chances are, the thief is mining with that and not trying to resell it. So you might need get some good suspects and then social engineer that situation for a while to get any answers.
You need a home alarm system, a mean dog, and a gun safe loaded to the gills my bitcoin brother...
I don't see how the guns would have helped... but the dog and security system sure could have!
Few ideas.
1) Identifiable codes/marks/IDs on the unit? Could ask Avalon if they'd have any record of such?
2) Clarify the position of ownership if someone discovers they've bought a stolen unit. By law it would be returned to you and they'd be out of pocket, so you'll need to give them a real incentive to report it [other than legal]. Sucks but its the truth. Ie you'll make sure they wont be out of pocket
3) Your mining details. When someone plugs the unit in, surely it will mine for a few seconds to your account, sending a few packets and location. Although I guess they could config offline first.
4) Get in contact with Avalon. They may have other methods of tracking or identifying the unit even we don't know about yet.
Holy crap you are smart, that's brilliant. Perhaps the mining pool could help trace his IP. I would attempt to pursue that for sure if I were the victim.
The Bitcoin community isn't big, I guess there is still a chance to catch that guy.
Hopefully he can narrow it down more than that!!