I might be totally out to lunch—and you old persimmon hands please reprove me for my ignorance if I am—, but I’ve never heard reports of Giombo being particularly hardy. In eastern Kentucky, you will likely be disappointed sooner or later. Unless you are at hand with ample protection, it just takes one good late freeze (like happened in 2020!) or one especially hard winter, and your work’s undone.
Personally, I’d keep an eye peeled for a good hybrid such as “Mikkusu” (aka JT-02), which reportedly gives you the flavor of an excellent Asian astringent with the hardiness of D. virginiana. If you want to trial a pure kaki, stick with the hardier ones, plant in a sheltered location such as near a sunny southern wall, and be prepared to provide some protection in case things go extreme, especially when the plant is young and small.
This thread is a great resource: Persimmon Cold Hardiness Resource (BTW, a search for “Giombo” in the thread does not turn up any promising reports—only one that it died back severely at -1.5F in MA, and another from AR reporting extremely severe dieback on a mature one after a winter vortex low of -7F.)
Of course, none of these numbers is absolute; and things such as degree of dormancy, tree age, specific planting conditions, etc. can impact a tree’s tolerance of temperature extremes. For instance, Chinebuli, reportedly the hardiest of the non-astringent Asians, has survived some pretty impressive temperature lows in Jackson County, whereas it died for a grower in Lincoln County in a pretty standard winter. You roll the bones whenever you plant anything—even when you think you’ve got loaded dice!
It’s worth mentioning that some folks successfully keep persimmons as potted specimens. To me it seems like a lot of work for modest production, but everybody’s got different goals and interests.