Hi D L,
you are right to point out that these characteristics can also be inherent and are not necessarily a product of any particular recipe.

You call your charcoal, (an interesting idea), an aggregate, comparable to sand, crushed seashell or gravel.... Why not a filler in the category of straw or flax...?

Here is what I have found are some of the working properties.
Too much sand and there will be no strength.
Not enough sand and cracks will develop.
Too much water and there will be excessive shrinkage.
Too little water and the mixture will dry out overly fast and not harden or adhere properly.
Mineral additives, namely vermiculite or too much lime in my experience, weaken the bond of the clay.
Albumen, egg white, casein, are examples, increases the fastness once it has dried, that is it will not give off dust when you rub it so much.

It will be interesting to hear how your bricks come out when dried.

Don Wagstaff