Guys... it gets even worse.
I had some free time today and decided to open up my headlight assembly.
After two more fuses blew last night, I...
fed up.
Okay:
Fuse removed, measuring against ground: 0 ohms for the left headlight, infinite ohms for the right headlight.
Okay, so disconnect the plug from the entire headlight assembly... Resistance is infinite... The cable is fine.
Then I'll take a peek inside the open headlight from behind... AHA!
A delicate yellow cable cheerfully rubs against a metal tab inside the headlight.
Awesome construction

.
Hella deserves some praise for that.
I insulated the cable and added some padding (foam) for protection.
Everything assembled, but the resistance is still infinite... great.
Licht an......funzt!
Meine Vermutung ist nun, das die Fuzzies in der Werkstatt eine vollkommen intakte Birne in die Tonne getreten haben und ich 180 Euro bezahlt habe für eine neue...die ich nicht brauchte....
If you don't do everything yourself... grrrrrr...
But perhaps it will help you, as the construction should be similar in most A6 models.
Because it is still physically very unlikely for a shielded gas arc to break down. Also, the power supplies are actually quite robust.
When replacing bulbs or ballasts, you inevitably touch some wires (the short circuit disappears)... and magically, everything is working again.