Nice mistery, the big problem is the geometry. You are right the angle is extreme. yes, the thickest shims at 4.5 sounds right, and the cups are only so deep. Measure the height of your valve head. We can get a measure of that to compare. Two measurements maybe, one for the top face to the top of the spring retainer, and one from the retainer top to the rotator top? What size adjusting wrench do the balls need? Maybe wrong balls? New ones are 17mm, old style is 14mm and I don't know if the deck height is different or if they are interchangeable. That is a good measurment too, the height of the ball base off the head deck.
No matter what the root issue is, Its hard to imagine someone left the gap so large. I can imagine someone leaving a .015 to .020 gap, but why leave a uniform .035? I can't think of anything that would allow the valves to change that much from where they should have been, except someone installing short valve stems, short balls, or thick seats. hopefully its a ball probelm. If its valves, we won't know which until you pull the head. Its not too challenging. I just r&r'd my head gasket. one day off 2 days on. there are only 3 or 4 gotchas to learn. The late 280sl have the cooling slots between bores. Mine were in dire need of clearing and with 100K and 40 yers on the old gasket, it was getting soft. I feel a lot better driving in this 110 degree heat today. worth the peice of mind.