you can connect 2-3 fans to a single header (using simple splitter) without worries. most of the headers are rated at at least 1A. a single fan consumes much less. something like ~0.2-0.3A at full speed.
If you are too worried, get a powered PWM fan hub - it's about 10-15$ from silverstone, swiftech etc.
so basically you can have any amount o controllable fans.
what you actually want is:
1. add two front fans as intake - preferable static pressure optimized fans
2. add another fan to the top (close to rear) as exhaust.
to have positive pressure in case (much less dust gets in) set the front fans to spin ~15% faster than exhaust fans.
About your idea of using G12 - it's actually nice one. you can reuse this on the next card as well. though mounting it will void the warranty on any card, but the ones made by EVGA.