Now this iPhone 3GS tried to compete against the ground...
...and lost badly.
To get the shattered screen off, I removed the two screws near the USB-port and placed a small suction cup on the lower half of the display glass (took some tries as the cup didn´t grip too well due to the fractures). After tearing gently I got the screen off (work extremely careful as you will have to remove three flex cables on the right side of the SIM card slot -> marked with orange labels 1, 2 and 3)
After removing the screwed LCD module and storing it in a safe place, I applied some heat (around 90 °C) to reflow the adhesive under the display glass. I removed it, cleaned its frame from glass shards and remaining glue and placed new adhesive pads:
Here the repaired display before reassembly (just put things back together as described above - vice-versa of course...):
Regarding repairability the iPhone 3-line was really a touchdown.