As a plumber, I can only say that I think it's slightly insane to build a bathtub out of porous materials.
"301.1.1 Approvals. Unless otherwise provided for in this code, all materials, fixtures, or devices used or entering into the construction of plumbing and drainage systems, or parts thereof, shall be submitted to the Administrative Authority for approval and shall conform to approved applicable standards acceptable to the Administrative Authority, and shall be free from defects. All pipe, fittings, traps, fixtures, material, and devices used in a plumbing system shall be listed or labeled by a listing agency or shall be approved by the Administrative Authority when listing or labeling by a listing agency is not available." - UPC
As to your immediate problem, the only way I can see to accomplish what you want is to chamfer space for the waste and overflow.