You've got the CIS-E fuel injection system on your car.

As these systems age, small vacuum leaks occur and the idle can drop + you'll get rough running at idle. When the car is cold, there is an enrichment circuit, which masks the lean out condition.
If you put your car in gear, hold the brake, and lightly step on the accelerator until you see 650-700 rpm (not 6k or 7k as you mis-stated), does your car smooth out?

There are two quicky adjustments that can be made to compensate for the air leaks.

One is to adjust the CIS unit itself. There is a tower between the air intake plate and the CIS head which when turned clockwise, will richen the mixture. I think it's a T-15 torx. Some still have the adjustment hole capped off, once opened, you push down against a spring, then turn slightly, maybe an eighth of a turn, and see what effect it had on the car.

The EHA can be enrichened also. Remove the EHA (two bolts), be careful system is under fuel pressure. There is an adjustment under a screw that you can turn CW to enrichen.

If you don't have a decent understanding of the CIS system, you should have this done by someone who knows how the system works. It's easy to overdue, small adjustments make a difference. Too much and your fuel mileage will drop precipitously. Do some research online and you'll find lots of info on these two adjustments.

This is a band-aid approach to a system problem, but it's a low cost adjustment that can make a big difference in the idle quality.

I just did this on our 560SEL, made a significant improvement. I'll probably tweak it a bit more when I see my buddy with an O2 sensor next week.

Jim

__________________
14 E250 BlueTEC black. 45k miles
95 E320 Cabriolet Emerald green 66k miles
94 E320 Cabriolet Emerald green 152k miles
85 300TD 4 spd man, euro bumpers and lights, 15" Pentas dark blue 274k miles