Is it likely my A4000 is freaking because it is looking for DF0 and CD0?
Yes, I think it's the CD drive. Move CD0 from SYS:Devs/DOSDrivers to SYS:Storage/DOSDrivers to disable mounting the CD drive.
The lack of floppy drive will cause a delay before the system starts booting, but once Workbench is loaded not having a floppy drive shouldn't have an effect.
I'm a bit confused how your replacement PSU doesn't have a power connector to fit the CD drive, though. I don't think I've ever seen an internal power supply that *didn't* have such a connector.
