update #2:
Reading some web review stating that the second layer of the Direct Power thingy is some kind of isolation made me a bit bolder, I also checked with a voltmeter, there is no current getting through to the PCB. Thus, after another good night's sleep I proceeded:
The rubber spacer needs a little cutting.

Just to be extra safe, I added a small piece of cardboard, cut to shape and glued on with a tiny blob of thermal goop.

The rest of the procedure is pretty straightforward. I like the fact, that this card is so small, leaving a big area of the heatsink unrestricted.

I did not trust completely in this construction. I still have a disused but functional old PC in the basement, which acted as a guinea pig. (Not all connections are done yet in this photo)

(I would not have been able to close that case...)

Nothing bad happened in a test run, so I thought, I would give it a try in my main rig. Mounting the fans first (NF-P12 PWM and NF-S12A ULN)

At long last, the card found it's way into the case.

It works and I'm happy, that I did not have to sell off the card, just to get another one, which fits the cooler.
PWM does not work with standard PWM fans. I put a PWM splitter on the sys fan header, which is now running the exhaust fan (bequiet silent wings) and the NF-P12 on the video card. The NF-S12A is connected to the fan control and dialled down to 600 RPM. I like the silent wings fan a lot as an exhaust fan. It's pushing enough air but does not have this droning hum, when ramping up.
So, how does it all work?
It's great.

In idle the loudest part of the rig is now the HDD. It spins down, when not accessed for a while, after that, it's inaudible, even at night with no noticeable ambient noise. Changing the exhaust fan was a good idea, the PC is now standing in it's original place with it's backside close to a solid wall and for the first time ever, I just can't hear it at all.
When stressing just the CPU (P95), there is a very gentle whoosh.
When stressing the GPU (furmark), the whoosh becomes substantial (coming from the CPU and exhaust fans, which cover the noises of the GPU fans), but well, the fans have to get rid of all this heat somehow. Compared to the jet-engine sound of the Asus fans, this is very, very good.
Some numbers of synthetic testing: (stating temp-PWM percentage-RPM; power draw in W; please note that GPU PWM and RPM also apply for the back fan)
idle: CPU 32°-40%-328RPM GPU 33°-37%-521RPM
GPU only, power limit 60%: CPU 50-60-813 GPU 60-56-792
GPU only, power limit 80%: CPU 51-63-860 GPU 67-60-843; 320W
GPU only, power limit 100%: CPU 49-58-803 GPU 73-68-945; 355W
GPU 100% CPU 3 cores p95: CPU 53-69-930 GPU 73-69-968; 428W
Adding more cores resulted only in more power draw, the temps stayed in that region. The PSU (Seasonic X-400) could stand 440W (furmark + 7 cores P95). When I added the last core to P95, things got sort of unstable, the system limiting the GPU power.
In real world scenarios everything is fine. I let Unigine valley run for a while: power draw is around 320W, the temps are in the low to mid 50s for both CPU and GPU with just a gentle whoosh coming from the fans.
This is, how I wanted this system to be all the time, I'm a happy camper finally! Thanks again everybody for your input!
edit: typo