I've heard that you can just take something like that to UPS and have them pack and ship it. That way if they break it, there should be no questions regarding an insurance claim.
Eh...if you try this, make sure you understand what's happening. The UPS Stores are NOT part of UPS, the shipping company. They are individually owned and operated. They may have a guarantee on their packaging, but I've heard tell that when something goes wrong they often try to point the finger at the shipper (UPS), while UPS tries to point the finger at the packager (UPS Store). End result, you have a hell of a time collecting.
I know from personal experience that some UPS Stores are ethically challenged (I had one place tell me that I had to use 2 day to ship on the receiver's account number. This is a complete lie, and other locations didn't even blink when I sent stuff by slow ground on the same account).
If you've got an ethically challenged UPS store, you can bet they'll do all they can to try to pass the bill for replacement onto UPS, while we all know that UPS often tries to push back on the packaging whenever they break stuff.
To my knowledge there is NO place that you can take an item, have them pack it up and ship it, and have them assume all responsibility, is there? I'd pay good money for that service sometimes, but right now it doesn't seem available.
Perhaps I've discovered a business to go into!