Any idea what the problem might be here?
Many IDE/CF-adapters do not have jumper for master/slave setting, and by default operate as master.
However, it appears that yours do have a MASTER/SLAVE jumper, so the one set as master goes to the end of the cable and the slave is attached on the middle connector of the cable. You can try this without the 4xIDE thing, just attach the cable directly to the A1200 IDE. If this doesn't work, there's something wrong with either the CF-adapters or the cable (neither very likely). If it works, try again with the 4xIDE, again with both CF-adapters on the same cable and make sure to use the primary port.
A second option is to use the other secondary port of the 4xIDE for one of the adapters, with both cf-adapters set as master. But then you either need to load the "ATAPIismajik" rom module described above, or use IDEFIx, to activate the second adapter.
As mentioned, many CF-adapters don't have slave/master jumper, as was also the case for many IDE devices at the end of the IDE/PATA era. The trick is that by this time, one had figured something called Cable Select (CS) where devices set themselves to slave when located in the middle of the cable. Nothing had to be done on the IDE controller for this, just a special "cable select" cable and at least one CS-aware device that can set itself to slave, so his also works with A600/A1200.