My Cossie did misfires under boost when the cable from alternator to battery was loose. It obviously also didn't load the battery properly. Don't know if this is the case here though, it sounds weird if it first misfires on boost, and only after that starts misfiring on idle. If you restart the car after that, can you then drive without misfires off-boost?

Is the battery fine, does the alternator load it correctly? If not battery voltage related problem, then it maybe sounds like it's fuel system.