Based on what you wrote, I would look at the vacuum lines. There are many of them, the idle air bypass hoses to the injectors, the injector seals and the rubber donuts between the two manifold sections, upper and lower plenum.
How're the timing chain and guide rails?
BTW, I have a similar problem on my 420SEL which starts poorly and runs poorly, at first. I'm going to replace all the vacuum bits and pieces.
See sections 7.3 and 14.
http://mb.braingears.com/126_DISC2/program/engine_380SEL.htm
Page 4 has a good picture
http://mb.braingears.com/126_DISC2/program/Engine/107/M116_38/14-450.pdf
I'll keep you posted on my progress. I'm going to check my O2 sensor first by measuring it's output. If it's bad, I'll go for the generic 3 wire version and solder it in. Once that's done, I'll tackle the vacuum lines.
I have to get it in for a safety inspection first. It should pass with flying colors.