Nice story AH.
This is a clear cut case of desensitizing, that siren is something that perhaps could do with a tweak in the twin star.
Other light twins have a siren that will only sound with a combination of events, that is 'gear up' and 'less than 10-15" MP'. So the siren will go off on a clean stall which is annoying in a trainer, especially if it finds itself stalling regularly. It is however, absolutely essential for reminding you that something might be very wrong on very short final.
That said, i must echo aileron_69's sentiments.
it all comes down to making you have a rhythm that you get into where you are doing everything in the exactly the same order and at exactly the same stage of flight every time.