In one aspect, a scrubber brush assembly is provided. The scrubber brush assembly includes a scrubber brush having a body of open-cell foam including an interior surface, a sleeve received in contact with the scrubber brush, the sleeve including peripherally-spaced, longitudinal walls and reinforcing segments interconnecting adjacent ones of the longitudinal walls and forming elongated pockets along the length, the sleeve having raised ribs extending along the length, and a mandrel having recesses formed on an outer surface, the mandrel being coupled to the sleeve by receiving the raised ribs within the recesses. Scrubber brush subassemblies, high stiffness mandrels, and methods of assembly are provided, as are numerous other aspects.