I am thinking that you could possibly have a leaking injector. Not much, but as it sits and idles, that cylender finally loads up and when you start off, it cleans itself out. Above 2000 RPM the leak is not enough to cause a problem.
When you have time, let the car idle until the problem starts really acting up. Stop the engine and remove the spark plugs and look for one that is wet with gas, or is black with soot. If you find this, then at least you have found the cylender. I would then swap this injector with one of the others. Also swap this plug with another one. Don't swap the plug and injector to the same cyl.
For example, If you find soot or gas on #3 cyl, then swap the injector with the one in #2 and the plug with the one in #4.
Then drive the car a few miles and when you return, let it idle again until the problem returns. Check the plugs again. In the above example if #4 plug is wet with gas or very sooty, then replace the #4 plug (or all of them). If the problem is now in #2 then replace the injector. If it is still in #3 then you could have a fuel dist problem.

If none of the above helps you then maybe it will help someone else along the way.

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84 500 SEL (307,xxx miles)