You won't find a mixture screw on the carburetor of a factory 280se because there is no carb.
the E in the name is for some German word for injected I'm pretty sure. But you sound like you are on the right track.
Normally there's a screw or plastic cap on top of the hole/tower for the mixture screw, which is normally a 3 mm Allen bolt. Righty-richy, lefty-leany. Don't go nuts! A 1/4 turn could mean burnt valves. I suggest taking the Allen wrench to DMV with you. Don't leave the Allen key in there. The Weight of the Allen key itself can cause it to run richer.
I think the simple way to do this is turn it left (counterclockwise) until it starts stumbling (lean), and then turn it about an 1/8 of a turn back clockwise.
After messing with the mixture you may need to adjust your idle, possibly even your timing. When you mess with your timing you will probably need to adjust your idle. I view these as: mixture > timing > idle.
I am not a mechanic or expert, just a hobbyist, and I am VERY often wrong.
PS: I had a similar experience with my 450slc 5.0. I could have gotten it "antiqued" but I wanted to make sure it was running right and used DMV for its free emissions tests. I was getting really rich running with 4% CO and higher. First I knew I had fuel pressure issues because the car had trouble starting often. It turned out that my accumulator was so horribly bad and leaking back to the tank that it caused the car to not start. Low fuel pump pressure in a k-jet leads to a rich running condition. I had hope that the accumulator would fix everything and get the mixture back to the way it should be. I was very surprised to see it had little-to-no effect on the emissions tests. Finally I turned the mixture screw and came up a total "0.00" on the CO and maybe even the HC too. When I got home I turned it just the slightest bit to rich. I should take it back through for an emissions test one of these days, but I kept it just a little more rich than those 0.00 because the engine in my car is one of the things that makes it special being an early 5.0 alloy engine. Richer is safer than leaner I think.