Got it to work
As mentioned before, the pin grounding method is indeed time-critical. The time to reset the oil counter is exactly 3 seconds, not at least 3 seconds (which is how I interpreted it). Apparently the circuitry is more sophisticated than I thought.
The procedure that I used which worked on my 6/99 build:
1. Put the key in and turn to position 2.
2. Go to the connector. Stick one end of the paper clip firmly in either one of the two pins.
3. Put the other end in the other pin and count to 3 seconds, then pull it out. You may need to practice a few times (i.e. have the paperclip bent correctly) so that you make clean contact the minute you stick it in and so that you can pull it out exactly after the necessary time has elapsed.
4. Turn key to off, then position 1 - and my car now shows "service inspection 15### miles" as expected.
Again - the key is to keep the pin grounded for precisely the ammount necessary, no more, no less.