What if instead of trying to grab the bits from the outside, you created a set of bits that had a square or hexagonal inset on the back. Then the extender pokes into the bit and the pokey part might be stout enough to not strip or deform under torque?
That would require that your bit-sets support having this hole, I suppose, but maybe you could also have small adapters that could be soldered or sintered onto the back of an existing bit set?
Maybe much more trouble than it's worth?
