Hmm... I had forgotten what the 1080 monitor was. A quick google says it's just an early version of the 1084, so a 1084 Amiga monitor cable would be your best quality picture. (And should be quite a bit better than composite)
I don't have a 1084 handy, but I think they used a 9-pin Sub-D connector. (Looks like a joystick or 9 pin serial port) So, the C= 23 -> 9 pin cable should be the ticket.
