Have you tried some fuel system cleaner? maybe just as sample as that.

Before I had the same sudden shudders plus rough idle when cold, they all went away after I used one bottle of fuel system cleaner. My car is a 92 400E, I spent $1000 for parts with no luck, finally $10 cleaner solved the problem.

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99 BMW 540i 6-speed 110K Km
03 SAAB 9-5 wagon 80K Km
92 400E (Sold) 245K km
Still missing the days with the Benz, it kept me busy.