Grafting higher up is fine. You may end up with an ugly junction, but the scion should grow. you will want to remove other branches close to the graft to make sure the tree's energy is going into the graft.

Orchards will sometimes 'top work' an entire orchard if a new and promising variety comes along. One example would be the Haas avocado. They top worked tons of mature Fuertes to switch over to Haas.

Key point is making sure the cambium lines up.

Here is a link that might be useful: top working apple with nurse branch

With a mature tree as the root successful grafts will grow very quickly. So if, after gathering your information, decide grafting high isn't desirable you can graft them low and should only have to keep them fenced in for a year or two. In that time your grafts may have grown 5-10 feet depending on species, rootstock, variety, etc.

I grafted several European plums to what I believe to be Green Gage tree and some of my bark grafts grew 7 or 8 feet in one season.

Grafts on well-established rootstock, as murky indicated; may grow VERY vigorously - and may be especially subject to being broken out by wind or perching birds, so be sure to stake or support them in some manner - especially if you're using a bark graft or simple whip - these work well but initially have very little structural strength.
Biggest problem I foresee in high-working persimmons unless you have a very vigorous, shoot 5-6 ft tall, with no side branches(which you might have, from those bush-hogged older trees), is that they're very obstinate about pushing growth on the existing framework, to the detriment of the graft.
I've done it, but you have to be very diligent about making sure that the graft is able to maintain apical dominance - I'd have to visit the tree at least weekly to pinch out/break off any apical growth on branches/shoots below the graft.