I guess there's no perfect solution that is both cheap and certain. I too have had good experience with Greyhound, but many locations limit insurance to $300. I've only had damage with UPS, but I have encountered goofy counter service with FedEx.
Surprisingly good shipping option
When FedEx wouldn't take my package for C.O.D. shipping, I went to the Post Office. They are shipping my Linn Wakonda from Phoenix to Houston in two days, and collecting payment all for $28.80! FedEx was going to charge me $52.68 if I had a shipping account! For next day by noon service the post office would still have beat the FedEx two day price by almost $10. When you bring your box to the counter, you needen't fill out any forms before hand, the COD forms are kept behind the clerk's counter. When you ship COD the insurance is automatically inluded.
The Post Office! Who knew?
The Post Office! Who knew?