Normally the connectors are different for drives that fit as a floppy disk (34 way double row edge connector) ATA/IDE drive (40 way) or scsi (50 way, or mini-centronix type connector).

So if your ZIP drives have the same connector as the Roland, and I would expect this to be 40 way double row, I would expect them to work.

Make sure the ribbon cable is connected 1-1, 2-2 .. 40-40 - don't assume that the connectors on the roland and the zip are the same way round.

I'd expect the Roland to expect that the ZIP drive is set up as a Master. The IOmega
The IOmega "integrators" manual has a nice diagram in it: http://download.iomega.com/english/manuals/english/en325401.pdf

Can you check the drives in a PC?