Excellent recapping job, LazzarusNine!
Take the drives and put them on the LCIII (though this may not be possible for the P630 drive as it is IDE and not SCSI), and install the system from there and put it back in the 475. You would need to partition and format on the LCIII before installing the system. If the drive is bigger than 2GB, you need to divide the hard drive into 2GB slices as that is the limit for System 7. When installing the system, if there is an option for it, select "for any Mac" and not "for this Mac." this will install a huge system that will support most 68K Macs, and you can trim this down later when it boots on the 475.
If this problem happens again, then the problem is with the floppies and not the floppy drive. It is installs cleanly, then there might be a problem with the floppy drives on the 475 and 630.
Take the drives and put them on the LCIII (though this may not be possible for the P630 drive as it is IDE and not SCSI), and install the system from there and put it back in the 475. You would need to partition and format on the LCIII before installing the system. If the drive is bigger than 2GB, you need to divide the hard drive into 2GB slices as that is the limit for System 7. When installing the system, if there is an option for it, select "for any Mac" and not "for this Mac." this will install a huge system that will support most 68K Macs, and you can trim this down later when it boots on the 475.
If this problem happens again, then the problem is with the floppies and not the floppy drive. It is installs cleanly, then there might be a problem with the floppy drives on the 475 and 630.