Now the question is... how do I actually get AmigaOS to see it?
Actually the driver should mount the partition once it is loaded. If it doesn't you have to use a program like Mounter which comes with OS 3.9.
Not only that, but how would I go about making it so that I could use it as my only drive?
You can't. A driver for a bootable controller needs to be in a ROM. The Mediator does not have such a ROM, so it's not bootable. You have to boot from a floppy disk or another harddrive on a bootable controller, then you can load the SCSI driver and mount partitions.
You are right in thinking that LoadModule could make the driver resident. If the driver supports that (and mounts partitions), that is. This works after the Amiga has booted once. But after power-on you have to boot from a controller with ROM, otherwise LoadModule cannot be loaded.
