The PC floppy drive hardware is designed to convert sequences of pulses received from the drive head into a data stream in real time. As such, it must instantly decide whether each pulse is large enough to be detected, or should be rejected as noise, before it has a chance to observe anything beyond it.
It one has a floppy drive which has been modified to feed the drive-head signal as an analog output, and allows finer-than-usual control over drive head motion, it may be possible to extract data from disks that cannot be read via normal means. I've read of hobby projects to construct such things, but I don't know of any that would be practically usable outside the hands of data recovery services.
As a compromise, there are some devices which interface with conventional floppy drives but precisely capture the timing pulses received from them. I don't know how well the decoding software can deal with data errors (e.g. if any pair of pulses should be separated by either 2, 3, or 4 microseconds, a conventional drive might try to classify anything between 2.5 and 3.5 as 3, but if a track has two consecutive pulse intervals that are 2.4 and 2.6 microseconds long, while all other intervals are either less than 2.2 or greater than 2.8, recovery software might be able to conclude that particular edge is misplaced, and use the block checksum to determine what it should have been).
Software-based recovery tools may be able to extract data that would not be possible from Windows, but hardware-based tools with various levels of sophistication may do better. Unfortunately, while I would probably have the knowledge needed to build such tools, I don't have any information about how to find them.