one of my gpgpu open rigs has a bunch of sapphire extreme running bamt, overclocked to 950/300 on stock voltage, but that is no guarantee that any of your chips should reach this as well.

If your system hardlocks to the point where you are unable to nothing when you try and overclock any of the cards past 850 I would expect PSU to be issue.
Are you overclocking using bamt.conf or do you do it manually? if manually, which program?

Keep an eye on dmesg for errors.

Do you have a single core CPU?