Actually, IIRC, the dwarves managed to recolonize Moria in the 4th Age.
Dennis L. McKiernan's The Silver Call
was written originally as a Middle-Earth story about the reconquest of Moria. When his publisher couldn't get the rights from Tolkien's estate, he filed off the serial numbers, and his fantasy world of Mithgar was born. If you read it, and squint just
so, the book works as a tale of the Fourth Age.