Rough Idle
 

Please Help, I have a 2005 R52 Base model with 199,000 miles. a few months ago it developed a rough idle and sputtering at all RPMs I suspected bad gas. However after adding the appropriate gas additives it got much better at high RMPs but not at idle. I cleaned the K&N filter and I have since replaced the following: Fuel filter-Mini, spark plugs-NGK, coil pack-Beru,(wires replaced 2 years ago). Fuel injectors-Bosch, fuel pressure valve, Vacuum pipe/line-Mini, throttle body-VDO, were all original, so I replaced them. The fuel pump was replaced about 6 years ago(90,000 miles ago), BUT STILL rough idle, some sputtering upon acceleration up to 2000 RPM after that it runs fine. My independent Mini mechanic has put the car on the computer and all numbers and figures are within specs. He has not been able to figure it out. The frequency of the rough idle is inconsistent and varies from all the time to very often. It seems to be worse when the engine warms up more than when its cold. The rough idle variation is from a steady 900 RPM to a drop of 200 RPM and then back up to 900(my normal idle RPM). Also it makes no difference whether the A/C. is on or off. With all the collective knowledge out there, what do you think it can be? Thank you.