On my 87 with the OM603, I ran into the same problem and it was my motor mounts. The vibration and shaking were very different when I put it in reverse or neutral versus drive. I am guessing it was because of how the motor mounts had settled and the way it would torque the drivetrain in drive vs reverse. The shaking would also get worse after the engine warmed up (I am assuming because whatever hydraulic fluid was left in the mounts would thin out). Can you do a visual inspection and see if they are collapsed? I think yours would still have the hydraulic motor mounts like mine does.

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97 S500 (90,000 miles) - wife's car
87 300D (298,000 miles and a replacement #14 head)
94 Suburban K2500 - need something to haul firewood
83 300SD (343,000 miles) (sold)