Ok, I finally managed to copy things over. I ended up having to use the shell to copy the System.zip over to the CF drive. I then loaded up the Real Amiga Install disk image in my HxC and let the Amiga do it's thing!
So, now I have ClassicWB ADVSP v28 installed and running in my Amiga 1200. Only thing is, I have a B&W display - it's not in color for some reason. How do I get it to show up in color on my TV (NTSC)?