560SEL Rough idling problem

[kilyab]

I have a 1991 560SEL - 115,000 miles on the clock - with a rough idling problem. Car has been tuned, new plugs (old ones appeared to be 'clean'), cylinders checked for compression (all readings were 165+), car does not burn oil. When engine is started, it 'rumbles' as though it has a 'miss' on a cylinder or two; increase the rpm to about 1500 and engine smooths out. When the engine is warm, the 'miss' is still there, but less intense, less even more so if it is in gear. On long trips, mileage is about 18.75 mpg - using cruise control at 74 mph.
MB shops have suggested to me that the fuel injection management unit (my term) which sits on top of the engine may have to be replaced, and it will be EXPENSIVE - say about $2,400 for the BOSCH part, plus installation.
Could this be my problem? Where else might I look. I need help on this, as we really like this machine (it is in beautiful condition), Many, Many Thanks to any answers/comments.
kilyab