Meanwhile I received it and took it to my "Cell Phone Genius". They replaced already many screens of my previous iPhones 3G / 4S / 5 / 5S and always did a great job. This time they were scared and refused to do the job as they said that they don't have tools and experience for the iPhone 6 / 6 Plus. They didn't want me to loose the warranty. I forced them and promised that it's all only on my risk. After 24 hours they called me, apologized 1000 times and asked me to pick the phone up. They didn't manage to replace the screen and damaged the home button too. I don't blame them at all.
I took my 6 Plus to the Apple store and got it fixed for $139 plus tax although the phone obviously was opened before. Well - at least I gave it a try and know for the next time. :)