Hello Thorsten,
I really appreciate you taking the time to explain all the fine details so thoroughly. It's fascinating what kind of people you can meet on a LEGO forum. I was actually looking for someone exactly like you, a chemist or materials scientist who would wearily and wisely gaze down upon my messages from the top of a hill.
To be honest, I'm simply afraid to use even a weak acid like vinegar, as I feel it could quite possibly ruin the prints, especially the ones with silver paint.
The main thing you confirmed for me is something I thought I remembered but still doubted, that distilled water does absorb the salts back. Even if it won't remove them as effectively as vinegar, it still makes perfect sense to give it a try.
Thanks again!