Replies to all, as well as more info:
1. Yes, I have tried composite video, and that works fine on everything I've tried, I just want color
2. My monitor does support sync on green, but also supports a separate line for composite sync, and is set correctly (as opposed to H and V on separate lines). I am getting somewhat of a sync connection, as the monitor rolls worse when I unplug that connector. Really, it doesn't actually roll so much when the sync is plugged in...the picture is just fuzzy and bent all over the place.
3. The hackish cable I made plugs into the monitor end of the 1084 cable. My only source for a plug was a joystick connector, so in total, it's about six feet long, and in some parts, through some rather thin wire. All connections use the same ground. I think there might be a short in the blue and green lines, because when I plug red into the blue or green connectors, the appropriate color shows up. The A2000 itself puts out color fine, as it does show correctly for that brief split second on the 1084 when switched.
Tonight I'm going to exchange some parts, use shorten the wire length, and build it on a PCB, rather than out of soldered/tape wrapped splices and that joystick connector and see if I get a better result. One company sells an Amiga video -> 4 BNC cable, but I'm afraid to ask what the cost is, considering the price most Amiga stuff goes for.
