Swap your BPV with someone and see what happens. Part throttle can cause the valve to open and close or even cycle strangly. This in turn plays havoc on the ECU. I have run into this problem (exactly as described) with badly adjusted blow off valves and by pass valves..
Stop messing with the tune. If it does it stock then you have a mechanical (physical) problem. Although you may find some magical way to tune it out nothing you have added should make this a problem.