I'm not a brickologist, but wonder if these are clamp-fired bricks. The clay is mixed with coke or other combustible material, the bricks are assembled into a 'clamp' and fired, and the combustible stuff burns away, leaving a finished brick. One of Dad's friends, Noel Pycroft, used to make bricks this way on Hayling Island. This is different from kiln-firing where the clay bricks are heated in an oven.
Looking at your bricks, the light colour of the outside and the black interior make me suspect that they are clamp bricks which have been fired too quickly and at too high a temperature, leaving the middle unburned and soft. That's much the same effect as barbecuing chicken legs too quickly, where you get burned skin on the outside and raw meat in the middle.
It wouldn't solve anything, but my sense of curiosity would lead me to heat up a sample of the black part and see if it can be made more brick-like.
Is there any prospect of taking this up with the supplier or maker of the bricks?
George B.