Well, a slow format actually does destroy data, making retrieval of the data highly unlikely. Your best bet is to take whatever back-ups you have and replace what is missing with the back-up files. Do you know how to take the back-ups & copy it over to the HD areas you hosed? If it's on another Amiga computer, you could do the "Floppy & Sneakernet" thing, but you'd need to first get a list of all files missing on the hosed system. Then you'd get a list of all files on the b/u system & identify which files are only on the b/u system & copy those ones over to the hosed system.
Program data on Amigas are almost invariably within the app's main drawer. It's really better to have apps & data on separate physical drives, but I'm guessing you have an A2000, an older system, when HDs cost a major amount, where the apps & data are together.
I'm unfamiliar with the Quarterback program, but I believe it's GUI-based, not a command line interface. See, if you had done a "Quick Format", all that would've affected was table entries of file pointers & your actual programs & data would've remained untouched & been able to be retrieved with proper data retrieval programs, such as AmiBack Tools that I use. DiskSalv4 is not as intuitive, I feel. With a slow format, your data is in all practical purposes gone to that great Archive in the Sky, barring any high-priced forensic data retrieval techniques.
I'm going to be driving to NYC this Thursday to pick up my son to bring him back here for the Passover holiday, then driving him back after the holiday. If you could wait until April 12 in the evening, I'd be passing by, although I'd have to take I-90 instead, I could set you straight & fix it.