If I am honest though, I would like a bit of an upgrade in terms of performance. The 6570 seems to be similar to the 4670, and the 6670 has a truly massive heat sink and seems to be a risky option.
If you want more performance you could go with PowerColor SCS3 AX6850 1GBD5-S3DH Radeon HD 6850
, personally i wouldn't run it fanless for gaming, i would just strap 120mm low rpm fan with zip ties, im running a Passive GTS450 with a Scythe Kama Flex PWM (check sig), running @ 250rpm, in my HTPC never have risen above 55C, probably would in gaming... but also running the fan extremely low, a Scythe SY1225SL12SL 120mm "Slipstream" 500rpm Case Fan
or if you manage to find a Scythe Gentle Typhoon 120 mm D1225C12B1AP-11 (500 rpm)
(ideal for horizontal placement since it comes with ball bearing) should be more than enough to cool it, and be virtually inaudible.