"commercial persimmon strain" is also ambiguous, because it could mean
virginiana or
kaki, or one of the few alleged crosses of those.
In any case, there are some major challenges to trying to cross black sapote (
D. digyna is the official preferred species name, but the synonym
D. nigra is also commonly used) with either
virginiana or
kaki.
First off,
digyna is diploid (30 chromosomes), while
virginiana and
kaki are either tetraploid or hexaploid depending on specimens. While it's not impossible to cross diploid species with tetraploid or hexaploid species, it's probably going to require a sophisticated lab.
Next, most of the attempts to create a "family tree" for the
Diospyros genus have placed
digyna in a rather distant branch from
kaki and
virginiana, so they are pretty far apart despite being in the same genus. Not even the same clade (I'm also pointing out
texana here because it's another diploid species that I'm hoping to try to cross with
digyna/nigra at some point, as it's at least in the same clade):