I should have checked before posting this same topic elsewhere, but too late.
I have an 89 260E and started using 89 octane about a month ago. Presto: the shudder at idle is essentially gone.
In the past year, I have replaced my ignition coil, overvoltage and fuel pump relays (not for the rough idling though) but still had the idling problems. Switching to a lower octane to save money seems to have had a very happy, and unexpected, side affect.