All the details are here, I hope you like it!
This is a wonderful usage of Arduino, not seen before! A+
Fantastic! You made it look easy, but I understand some of the details you had to cover...
I once designed and wirewrapped a floppy disk controller for a (now) OldSkool computer. And it took me a LOT longer to get it to work!
Nice, hehe, chuck on a wifi/ethernet shield and host the data from a webserver.
Rather that trying to put a 720kb physical disk drive on your Arduino or use networked disk from a PC, I would think about getting a micro-sd (or sd) shield and use that as the disk drive (presumably copying the bits from the original disk drive). That way the unit becomes self contained, and doesn't need the PC nearby.