Equally long-winded answer follows: Don't let them convince you that the CLK fuel injection system is more delicate than the system found on your E320. I bet your problem is caused by the contaminated gas. Years ago we had a fuel injected shop car (280TE Euro) that was fueled with contaminated gas containing a fine white powder. Repair costs were $$$ due to having to clean/replace the entire fuel system a couple of times. The powder was so fine it bypassed the main filter and the non-replaceable filters in the warm up regulator and injectors and coated the insides of the entire fuel system including the hoses and lines.

My guess is you have a particulate type contamination that gets stirred up the longer your vehicle is operating and may be large enough to temporarily plug the in tank fuel filter. Once the car is shut down for a bit it settles down, the in tank filter unclogs and your car will operate normally for a time. I would contact whoever performed the repairs on your CLK to determine exactly what kind of contamination was found in your CLK's fuel system. Whatever it was it's a pretty good bet that that is your problem. Now the bad news---since the problem occurs only after an extended period of operation you will probably be the only one to diagnose whether the fault is fuel pressure related. If you feel comfortable doing this obtain a fuel pressure gauge and check the fuel pressure when the car is running properly and then keep the fuel pressure gauge in the car with you (detached from the fuel rail) and connect it when the problem recurs and observe the fuel pressure to see if it is substantially reduced/at 0 psi. If so, your problem should be solved by draining the the fuel tank and replacing the fuel tank filter and main paper fuel filter. You may also need to have the tank removed and professionally cleaned.

Now the obvious and not so obvious warnings: Proceed at your own risk. Don't do this if you are not competent to safely carry out these tests. Gasoline fires can quickly ruin your life. Have the proper fire extinguisher handy and know how to use it. Operating your car for an extended period of time with a fuel pressure gauge connected is a fire hazard and never operate your car with the fuel pressure gauge in the passenger compartment. Also, the fuel rail will/may have gasoline under pressure when you connect the fuel pressure gauge so gasoline WILL leak or spray when you attempt connect the gauge. Wear eye protection, wrap the schrader valve connection and gauge hose with a rag and connect quickly.

Good luck. Mark