Well, the thing is: Quick Format does not delete anything. That's the good news.
Reinstalling something on that partition, however, really starts deleting the important parts, like the File Allocation Table. Although some of your data is still there, if it is fragmented, it can never be put together again, without a whole lot of work. And you don't know what has been written over anyway.
W/o the reinstallation, you would have had a good chance. But with a reinstallation, your chances are close to zero, and I cannot recommend buying a recovery program. Maybe some recovery programs still have the option of checking what they can rescue for free, and the rescuing is done in the paid for version, at least that would avoid the risk of buying a useless program.