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Sadly you would not be able to get a replacement at a lower cost or be able to add insurance. If you bought it full price on a credit card, some card companies offer protection but not all. If you pay for it via credit card maybe you can check with them if it is covered. Sadly, beyond that, there really isn't another option.
Oh man! That is so sad theartiszan is correct though. There is no way to add insurance after the phone was purchased. This has to be added to the line at the time of purchase in order for the phone to be covered. In addition to what theartiszan said, you may be able to check with your home owners insurance to see if they have any personal property insurance benefits?