One differentiating trait they noted was that the poems go beyond personal narrative to frame a situation within a larger historical context. Once that larger context is in place, then the poet may "go through the small door" of family history to reveal the broader narrative (Nelson).
This afternoon, I'll present a workshop about documentary poetry, a related mode, yet one that occasionally stays within the smaller frame of the personal. Another difference is that documentary poems are not written in persona as often as Cliophrastic ones.
Thus while most Cliophrastic poems, since many are inspired and informed by primary source research, are simultaneously documentary poems, the documentary poems that stay within a personal frame do not fit the definition of Cliophrastic.
I drew the diagram below to illustrate the relationships between four modes of poetry as witness. The flower shape reminded me of the poem in Nelson's book about George Carver that is written from the perspective of a field of flowers.