Tried to return the card - no go at my supplier due to opened package.
Modding is the only option now.
Faustus is right about the screws.
I've dismantled the whole card basically, in this manner:
1. Remove the whole cooler by unscrewing the four screws around the GPU core. You have to wiggle it carefully for a bit for the cooling paste to release its sticky grip.
2. To remove the plastic shroud + fans (and the metal frame it's on) you remove two screws on each end of the heatsink, on the short sides. No biggie, but I had to use a screwdriver to 'unbend' one of the heatsink fins that was somehow holding it all together even without the screws. After that, the plastic shroud came off.
3. I removed the plastic shroud from the fans and the metal frame by removing the small blacks screws on the plastic. 2 on each long side, then 3 larger versions under each set of black/red metal decorations on top of the shroud.
Seems like the two fans are regular PWM fans that has those 4-pin connectors you see on GPU's. So no surprise there. They are both connecting to a Y-cable that goes into a 5-pin connector which is the one actually connected to the card itself.
Here's a badly lit pic of the result (at least I took the effort to clean off the old thermal paste while at it):

I'm thinking about getting two Arctic Cooling F9 PWM fans, and two of these:
http://www.gelidsolutions.com/products/ ... d=60&tab=2(thanks for tip SebRad)
Problem is, I can easily get the fans in a day or two from local suppliers but the Gelid cable is a lot harder to come by. Fastest I can do is send by airmail from 'quietpc.com' which may take up to 21 days. Better than nothing I suppose, and I can use the card in vacuum cleaner mode until then I suppose.
Edit:
I've been doing some reading in this thread here:
http://www.overclock.net/nvidia-cooling ... 70-hd.html..and the DVI cap they mention there is present on this card as well (Asus GTX570 DirectCU) but there are a few millimeters of clearance now that I've measured it 'naked'. We need 46 mm, and I measure 48 mm available.
So, a Thermalright Shaman seems like a possible solution. I have no idea what the connector on the fan for the Shaman looks like though. Anyone?
Also, I've read about some nasty clicking noise from that fan, so that doesn't sound promising. The cooler itself though seems to perform awesomely. I have yet to figure out if you need to fit that extra weird vertical 90 degree cooler (can't explain it better). Something like this:
http://www.inet.se/artikel/5321634/ther ... 5-heatsink