You don't need IDEFix. The Dataflyer and the CD drive are both SCSI. There are things in the IDEFix package that might be useful tools (FindDevice, CacheCDFS), but installing the whole package isn't necessary.
It's probably worth using CacheCDFS since the CDFileSystem built into 3.1 is terrible. It's possible that you had everything configured correctly but it just didn't work because the software is bad.
Other things to note: old CD drives tend to have a hard time reading CD-Rs burned at high speeds, and many can't read CD-RWs at all. When testing, try any professionally-mastered CD with data on it in addition to your file disc.