This tip is kind of hard for me to write because I'm very big on recycling any cardboard box that comes through my door and can't be used as storage (when you live in a small place and love buying new gadgets, they tend to pile up).
The officer helping lydiat was able to get the serial number for each item from the boxes, making it so if the gadgets are recovered, they'll be able to tell which are hers from the numbers. Of course, if you're short on space, you could also just cut the numbers off the boxes.
Sadly, even though lydiat has employed additional super-geeky ways to find her old gadgets, none have shown up yet.
Oh, and a lesson lydiat and I both learned from this debacle: get renter's insurance immediately.