Confirmation:
970 boards do not crossfire well with any combination of cards. This is because the 970 chipset can only do 1 PCIe @ x16. The 2nd card will be at x4 or x8. Pairing a slower card with a faster card will also slow the faster card down. Your best results will be with the single fastest GPU you can put in this board. (* Caveat - 990FX boards can do 2 PCIe @ x16 so they are best for AMD CPU + Crossfire or SLI)
Regarding FX 6300 + H60 OC:
The H60 is not a very high performance liquid cooler, but should be fine for your 4.4GHz target. For comparison, I've built an FX 6300 + Cooler Master Hyper 212 EVO system and hit 4.4GHz on stock voltage. Temps were good. You should be fine.
Now...if you want to get insane...(* MAD is in my name right?) look at the second half of my sig.
I've had an FX 6350 to 4.950GHz stable on a Gigabyte GA-970A-UD3P board (8+2 phase power). 4.8375 for 24x7. So, with the right board, power and cooling...the FX 6 core has a lot of potential and sits in a nice thermal/current sweet spot. The 8 core FX CPUs get a LOT hotter and draw a LOT more current to OC, making them more challenging to push high.