Status report: I've been slowly adjusting the Bowden cable over the last few days. I hesitate to say the shift problem is gone, because it's been intermittent: May have turned the adjustment nut two full revolutions counterclockwise so far. I can tell a difference. Will update as it becomes more certain whether I've hit the sweet spot in the adjustment.

J.M., do you want to add a cabriolet to your collection of W124s? Thank you for your suggestions.