You've done about as much as you can electrically. Next step is to remove the regulator from the alternator and see if the brushes are worn down to where they're barely making contact with the slip rings. You don't have to remove the alternator from the car but you do have to get underneath and remove any belly pans that may be in the way. Regulators are not expensive -- maybe $50 depending on the source.

Jeremy

EDIT: The photo shows a new regulator, left, and an old, worn (but still working) regulator on the right. As the brushes wear more and more, the springs can no longer push the brushes tightly against the slip rings and charging voltage is interrupted. Since your 1997 E300 is more electronic than earlier models, it requires a good, stable source of power. An alternator that is cutting in and out due to worn brushes or other problems could cause the stumbling you've been experiencing.

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"Buster" in the '95

Our all-Diesel family
1996 E300D (W210) . .338,000 miles Wife's car
2005 E320 CDI . . 113,000 miles My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970