Well hey that was a pain in the ass. Here are some protips regarding the old fat ps3:
Use an external drive for the backup. If you use the program above to format it in Fat 32 you don't have to abide by Microsoft's self-imposed limit of 32 gigs on the partition. I got one 93 gig partition on my external just fine.
Take the time to use compressed air and clean out the vents and stuff on the PS3. I take very good care of my electronics but found that a lot had built up over time.
Use a small flat screwdriver to pry up the edge of the cover on the side of the PS3. You must remove the blue screw in the center of the caddy first. After that, slide the caddy to the left, remove using the clip/handle.
There are four screws holding the drive in the caddy. This is important. If you remember nothing else REMEMBER THIS: The screws are very soft, very shitty, and unfortunately are screwed in very tightly. You must have a bit with a pretty exact fit to get these out without trouble. You will need to press the screwdriver in firmly to get them out. I had all but one come out. The last one rounded out and I eventually had to snag the edges with vice grips to unscrew it. It is a pain in the ass and is hands down the worst part of the process.
I'm restoring my backup now.