you wont need to worry about the EEPROM. In terms of HDDs, EEPROM is really only an issue if the HDD is locked. When you lock a HDD, a specific key is generated and stored in the motherboards EEPROM and is required to unlock the HDD. As usch if you put a locked HDD in another xbox it wont work with the different m/board.
However, actually locking the HDD does not require a code (the codes generated is for unlocking the drive). As such, you can take your new HDD, make sure its unlocked, remove it from your box, take it to your cousins place (or whereever), get your cousin to unlock his drive (just to be safe), attach yours to is DVD-ROM site, use the HDD upgrade wizard to prepare the drive. Remove your still unlocked drive and re-attach to your box. I would then make sure everything is working fine (ie apps and games), lock your HDD and then re-unlock it, then backup your EEPROM to the chip and .bin.
To prepare the drive by FTPing backups in from your PC, you'd firstly need to backup the complete C and E drives (drag the whole C and E drives onto your directory in flashFXP, not just the few files you listed in 'C:\backup'
You need to get the whole folders so you get all the files for you MS dashobard (C drive) and all your game save data etc from the E drive.
I've never used XOS to prepare a HDD and am not entirely sure how it would be done, but heres how I see it;
1) Install XBMC on your original drive and boot it. launch the syste info option and take note of the partition names and the exact size of these partitions on your original drive.
2) FTP into xbox with original drive installed. Drag C and E drives to PC desktop (I think the other partitions are only filled with files generated from these partitions.
3) Ensure old drive is unlocked, remove old drive, install new drive. Boot XOS and go into disk tool
4) things get a bit hazy here but I imagine you should be able to create a partition somehow. You'd need to create each partition according to the name and size you documented in XBMC. This will give you all your partitions except for your F drive. Hopefullly then theres some way of formatting the rest of the left of space in one partition and calling it F drive.
5) If you succeed in that, reboot XOS, FTP into the drive, open the Xboxes C drive, then open the C drive backup on your PC directory, select all the files in the PC directory and drag them onto the xbox C drive. Once thats done, repeat for the E drive.
6) try launching XBMC and your MS dashboard.