The 6670's cooler is quite good, barely audible at idle. Still, a hint of the bearing noise can be detected if duty cycles goes above 55%. What kind of replacement fans do you have in mind, and how would you attach it to the card?
By the way, do you know if CCC's fan speed control work?
Indeed, it was mostly bearing noise that made me swap the fan on my 4670. If the stock fan is 4 pin PWM it might be best sticking to PWM and let the card control it. Arctic Cooling makes some decent 92mm PWM fans though any half decent sleeve bearing or FDB fan should be an improvement over stock.
To mount it, I used silicon fan bolts which were friction fit between the heatsink fins. It sounds flimsy but proved quite secure in practice. You could do it too since the heatsink is essentially the same. Zip ties, twist ties or rubber bands are also commonly used.
As for fan control, the best option would be to let the card control the fan. This means either finding an adapter cable (I remember seeing such recently, don`t remember if they were 3 or 4 pin though) or, removing the plug surrounding the pins on the card. I`m not really up to date with CCC so I`ll leave it to others to answer.
3. Given the proximity of card to the top cut out, would it make much difference if the fan is mounted on the casing
instead of being strapped to the card?
Yes, it would. A fan atached to the heatsink will be much more effective in forcing air through the fins, especially at lower speeds when air pressure is lower.