How can I recover important data files from floppy disks (3 1/2 inch) that were
inadvertently reformatted, in a low cost manner?

Your best bet is too try some data recovery software, download the
trial versions first and see if they can see your files, depending on
the software you'll probably have to buy the software before you can
actually extract your files.

Have a look at <a href="http://www.recoverdatafiles.com">Data Recovery
Emergency Room</a> or at the sponsored links on this page.

I've tired BadCopyPro and it works!

http://www.jufsoft.com/badcopy/