I have vario 2004 and here is my experience. This exact problem is related to AC load and outside temperature.
BTW If your RPM drops only by shifting to D without AC then it is another story.
Recently I noticed that RPM drop and vibration issue started with my vario only on AC. RPM is perfect when I shift to D or R without AC. Even if AC is on car is in P or N it is fine. But when AC and transmission both engage car goes mad. If car is in P or N with AC on and I give a slight push on accelerator RPM would go up and then it will frop to around 300 and again stable. No fault codes or other issues were found.
Then I started to noticed that if outside temperature is in lower range like early morning, the problem seems to fix itself. So I suspected that it is AC related issue. So I did a test when outside temperature is hot (40C) and problem is present. I put some water on AC condenser while AC is on and suddenly the problem disappeared.
I still have to find permanent fix for the issue. Maybe condenser wash will help