There actually are such a databases, kite. Unfortunately, each music store and pawnshop maintains its own and they do not share data. My keyboards were found by the music store itself, using their own database. My amplifiers, however, were not flagged by the retailer (Guitar Center) but found by me by accident. Guitar Center still has my ADAMs, because I could not find the serial numbers for them and could not positively identify them. That's OK, because they were damaged and I didn't want them back anyway.
If I had to do it all again, I'd keep my mouth shut and let the gear disappear. That would be my advice to anyone who goes through this. That was my advice to Beagle: don't go looking for your stuff.
Allowing thieves to get away with their crime is an unfortunate consequence, but as I found out it's easier to recover stolen property than it is to catch and prosecute burglars. If you do get your stuff back, it accomplishes nothing except to aggravate your own pain. I have suffered a financial loss equivalent to having had no insurance at all, making me wish I'd put my money into cameras and alarms instead of insurance premiums.
At the moment, I have still not reclaimed my stuff. I left a message at the PD a week ago Monday, asking where I need to go to get it, but they haven't returned my call. I'll send them an email next, in order to document that I tried.