Who is diagnosing that your o2 sensor is bad? Is anyone diagnosing it, are you just replacing it because you think that's the problem? Maybe you have corrosion in your connector, maybe you have bad wiring, maybe you have a bad ecu. Don't throw parts at the vehicle, diagnose it properly and fix it right the first time.
Do a boost leak test, fix and leaks you have, replace that BOV with the factory BPV and then see if your boost is still fluttering.
My car flutters in vacuum when just touching the gas but holds steady when at idle or when applying more throttle, I think it's something to do with how the gauge is plumbed in.... could be wrong here though.
Re do your compression test just to be sure.