Certain companies are much better than others, Allstate is notorious for being hard to collect from, even when it involves their own executives in their Zone office parking.
I believe in general you want to stick with the folks who insure your home, and use an Inland Marine Policy- though the only claims I have had were from damage, it covers everything baring an act of war.
Get a Good agent, and as they charge according to what you value, the big thing is to make a police report, to verify things were lost, it is a crime to file a false report, and then proceed as best as possible. Insurance companies do guard against fraud.
I too left my Leica CL, 28mm, 40mm, couple of Nikon SLR's, new gold watch for my mother, traveler's checks, passport -- well it was a Domke, at a restaurant in Italy, the waiter had pushed it under the table cloth and I just walked out.
When I finally tracked it down the next day, everything was in the bag hanging in the cloak room, and I handed the guy $20 for watching over it.
OTOH, a friend recently found a camera at Lowes, turned it in, and the person he gave it to never logged it in.
A friend found an M3 outfit in an airport, left his card with Lost and Found, and no one ever called, so he was honest, and he also ended up with an M3 w/ lens.
Fingers crossed for next time, and double good luck, glad you got your stuff back, when traveling it is amazing how much you might stick in a camera bag, I carry less now.
I have heard good stories about people returning stuff, I have done it.
Regards, John