My take on it is the turning left or right thing is the main problem => motor mounts.
It reminds me of this thread where turning one way caused a weird effect
Front Suspension Noise (VIDEO)
It has the best on car video I've seen so it is worth looking at the thread for that.
I say replace the motor mounts the transmission mounts and the flex discs.
Look on your prop shaft for marks to see if they are aligned correctly or not.
When refitting the prop shaft roll the car backwards and forwards (on its wheels) to allow for the rubber parts to settle before you tighten everything up.
Oh yeah and when you have the front flex disc off check the output shaft on the transmission - there have been reports of the nut coming loose.