You sound awfully calm, vestandpants. I'd be doing some serious torque wrench tossing about now! Perhaps a pint or two before posting?

It doesn't seem likely that the 6mm bolt/s would fail at the suggested 23nm setting. And you are sure of your wrench? Might you be able to borrow another wrench a do a test with some loose shop bolts? Perhaps confirm your wrench's performance.
It has to be frustrating for you. Were you able to extract the broken bolt/s? Was it the bolt head that failed or the shank?
My granddaddy, when asked how to torque bolts and studs properly, told me to, "Pull until it gives, then back off half a turn." Thanks, Grandpa!
Monte