Got one in my other 5.1, which has your card and a SC version under 10.10.3.
Drivers are nvidia's latest for both web driver and cuda. Also have a GT120 in that box as all it's used for is rendering. I have it coming into the RGB input on one of my monitors off the GT120 and control it from my main 5.1 via teleport. Works fine. That one is a stock dual 2.6 4 core. Had zero issues getting it to work. Formatted drive, installed 10.10.3 via FireWire transfer, installed the nvidia stuff while on the GT120, dropped the cards in and rebooted and started rendering. I do NOT think it's the card model. You might have a specific INSTANCE of the card that has a problem (quickly ruled out by simply putting it into another box), but I have 3 different variants of the EVGA GTX 970 ACX 2.0's including yours and have zero issues with any of them, under 10.10.2 and 10.10.3.
I think you're more than likely chasing the wrong issue as there are a lot of people using these card with the exact same drivers on the same versions of the OS without issue, so it must be something else. The simplest solution is to check the card in another box. If it's good there then it's either the box hardware, the power connectors, your installation hardware wise or OS wise. Can't be anything else.