hey Jeff. I'm think something might be grounding out. From My past experince especially for the early 124 V8 cars. The engine wiring harness gets really hot and brittle and falls apart. Its the main engine harness that wires all sensors,injectors what have ya. If you remove the aircleaner and inspect. Its possible some of the injector wires my be grounding internally under the insulation causing a lean idle misfire. Causing a indivdual cyl or cyl's to starve for fuel causing hesitation,backfiring, missing.
Its worth a try. I've seen alot of these. First hand experince on my 500E also. But I had the aux fan constantly running due to wires touching them selves. If you going to keep the car. I rec doing this. Also with that Mileage I rec new timing chain,Rails,tensioner.
Hope This helps Guido.
2006 Mini Cooper S
2009 E350 Sport AMG package