I still think it is an ignition issue. So if the plugs, wires, cap, and rotor are relatively new then I'm thinking coil. However, I would open the hood at night and see if there are sparks dancing around. If so, you'll know where the problem is. If not, do you have another coil to try?

And, if it isn't ignition then you are running so lean that it dies when you give it throttle. A very low float level could do that, or a plugged filter. You said you don't have a vacuum leak, which would also do it. Are you sure your intake manifold isn't warped from the overheating?