The problem isn't in the tires...its the WHEELS.
The e70 has a larger
wheel hub/center bore than the e53...you need to install hubcentric rings on the e70 wheels to reduce the opening from 74.1mm to 72.56mm...hopefully that will get rid of the vibration or at least reduce it to a tolerable level.
Again, the vibration is coming from the wheel not be centered on the hub...the opening in the e70 wheel's "center bore" is
larger than the hub on your e53...and since the wheels are "centered" by the hub (not the lug bolts)...the wheels are vibrating due to them not being correctly centered on the hub.
Below is a BMW wheel comparison chart that I cobbled together last week due to xDrive being offered on many of the models + the new "F" body BMWs have different offset ranges than older "E" body BMWs:
