We examine the process of cascading fragmentation for the Kreutz sungrazer system to continue our exploration of its birth, orbital evolution, and temporal clumping. We modify and broaden the two-superfragment model from Paper I to include clusters of ~30 bright comets spanning four centuries and 1000 SOHO sungrazers from 1996 to 2006. The spectacular parent sungrazer X/1106 C1 is assumed to have tidally split shortly after perihelion into a train of major protofragments immersed in a cloud of particulate debris, which at larger heliocentric distances were breaking up nontidally over and over again. We describe potential evolutionary paths for the Kreutz system by linking X/1106 C1 in subgroup I-type orbit with the comet of February 423 in one scenario or with the comet of February 467 in another. The latter scenario accounts for sungrazer clusters in as early as the 16th century, suggests that the progenitor object may have been observed as the comet of 214 BCE, is quite consistent with the orbital distribution of the SOHO sungrazers that sample the central filament of the Kreutz system between the clusters of major sungrazers, and predicts future clusters until ~2120. Comet X/1106 C1 and the common parent of C/1882 R1 and C/1965 S1 were two first-generation fragments of the progenitor that split nontidally on the way to its 5th century perihelion, reminiscent of the superfragments in Paper I. We provide computational tools needed for solving the problem of the Kreutz system's orbital evolution, but no unique scenarios are presented for the individual comets. Another cluster of bright sungrazers is expected to arrive in the coming decades, its earliest member possibly just several years from now.