I'm running 3x XFX Radeon RX 480 GTR Black and 1x XFX Radeon RX 480 GTR on one Rig using the latest Crimson driver and claymore's 6.3.
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So far the system runs more or less stable. What difference would a switch to crimson 15.12 make...?
Your RX 480s would not be useable anymore.

(supported from 16.6.2 on AFAIK)
Also, has anyone been able to achieve higher hash rates with the 480s using claymore than what I got? If so, how?
Yes. At least 26.6 Mhash/s ETC + 465 Mhash/s SC is possible on a (cheap and not so great) XFX RX 480 XXX without BIOS mod. More would be possible if the memory was not that picky.
How? Simply more undervolt, more overclock...