Sounds like you've done your homework on this and have replaced just about every related part possible.

The only other possibility that comes to mind, (as long as your SURE you dont have any vacuum leaks) is a leaky fuel injector or two. They tend to leak fuel as the car sits overnight, then on the cold start, the excess fuel in the cylinder(s) causes the rough running until the engine has run long enough to clear itself of the unburned fuel. Unless your able to remove the fuel rail and test the injectors, you may want to have it professionally diagnosed.

I also remember an oddball problem similar to yours a few years back. This was on an E46 but with same M54 engine. Same complaint and after chasing the problem for a while, it ended up being faulty intake lifters that were very slow to pump up when cold, causing rough running. Maybe also perform a cold comp. test and see what you find.

Hope this helps and let us hear back!

-Ben