Without SPI/ICSP access, your kinda stuck. The FTDI is only handy with the bootloader working, and it does not sound like this is the case. Your 16u2 sounds like it is ok, but I know of no one that has a sketch for the 8u2/16u2 to SPI out to the Atmega2560. Could be handy, but most seem to fry the 8u2/16u2...
You are either going to have to:
a) Get a ICSP programmer (No TinyISP)
b) Get a new Mega2560 board
c) Get that Uno you should have had before the Mega2560 
Sorry about the death in the family.