While we never had a shudder in any of our 4 740s except when front rotors were thin, this shudder was in the pedal.

Unless you have checked them already, check the tie rod ends, in over 300K miles in these 4 cars, the only suspension parts that were replaced were tie rod ends - perhaps 4 sets.

I once read that about 70 percent of vibrations start with the wheels - perhaps you should have their balance checked. A wheel weight may have fallen off - look for this?