Thanks for your answers, folks.
Unfortunately I tried all your suggestions already. Completely reinstall newest iOS on the new iPad, recover from backup, instead of setup as new device, wait until restart is complete. All via cable + iTunes on Mac …
Wish I could share your optimism. I tried it again yesterday - 3 times.
This time I even reinstalled the complete iOS 7.0.4 via iTunes before.
The last time I switched from iMac/MacBook to a fresh Windows which had never seen iTunes before.
Always t…