The phone is back from the shop. They replaced the mainboard. The GPS now works 1,000 % better than before.
=== Before ===
First lock with no aiding data, only 1/2 sky available: 245 seconds.
Second lock: 10 - 14 seconds.
Fix while in office 2 metres from big window: never
=== After ===
First lock with no aiding data, on;y 1/2 sky available: 74 seconds.
Second lock: 1.4 seconds.
Fix while in office 2 metres from big window: 2.4 seconds to fix
Bada Boom Bada Bing!
Glonass is showing, but after a good fix, it switches to just GPS. Fine with me, because it at least show 2 or 3 GLONASS while getting the fix and a short time thereafter.
So, if your GPS sucks, maybe you should try getting it repaired.
edit: of course, we will have to see what it does on a cloudy day or while driving. But still, the way the GPS found and fixed the location was waaay faster than before and I never got a fix at home inside 2 meters from the window before - never!
Stock D803 4.4.2 Kitkat