So what controls the idle if the ICV is disconnected? With the ICV disconnected the idle won't drop below 1k even with the throttle stop backed up all the way.
There's a rotating vane valve in the ICV. When the ICV is unpowered, it rotates to a fixed opening point. So it still flows air, it just doesn't control the flow. When you power it up it actually rotates to close that baseline opening and opens a gap on the other side of the valve.
I'm probably not explaining it well, but if you look at an unpowered ICV you'll see the opening where the air flows. The rotation of the valve is in the direction of making that opening smaller, not larger.
The throttle plate isn't supposed to be completely closed. There's a calibration to set the correct air flow at idle, but it requires Alfa flow tools that you don't have. Since it's been messed with anyway, maybe try *opening* it a bit more using the adjustment screw? It sounds like you're not getting enough air at idle, and if the throttle plate is too closed that might be part of the problem.
I would try progressively opening the throttle adjustment until it'll idle cold with the ICV connected, see if that makes a difference. Note that you'll likely need to adjust the TPS in parallel so that the idle switch is still closed at idle.