I quick round-up of this thread. The wheel (as described in the initial post) is built and all is well although the mileage is for now still in the double digits. Based on this thread (and a real life inspection by IanH) I came to believe that my project had two issues:
First, my spokes are a wee bit too short, maybe a 1-2mm. Not overly essential but it made the process more cumbersome.
Second, some spokes had a wrong nipple. I checked all the spokes and they all needed 2mm nipples.
My solution to both problems was to buy DT Swiss 16mm nipples, in 2mm and to replace all nipples. Worked like a treat. The wheel was finished in less than 1h. Thanks a lot for all your help!
One lefts-over is: How do you determine nipple size of the remaining 12mm nipples? Is there a quick&easy solution or is it guess and try with a calliper and/or different spokes?