I don't think you'll have much luck there. I trimmed my white sapote last week and the leaves wilt really fast. I doubt caterpillars will eat wilted salad that's been limp for days.

I find it odd that a species from Ohio would thrive on a non native tropical tree from central America?

I found this on a casual search of the web on my first hit:

Black Swallowtail Caterpillars eat Golden Alexanders (above), Wild Carrots, Celery, Parsley and Dill.

Wilt-and rot. Even in Dry California pruned leaves get a mold within a couple of days..thanks GNAPPI..its not my imagination!
Funny-but I noticed those big butterfly's early this summer..hadn't seen them for years. Great to learn that too!

Those are two different swallowtail species. The Giant swallowtail cats eats on citrus and sapote, I have both and they do prefer the sapote to citrus.
The other swallowtail you are discussing is not the giant, but rather just the black. I grow fennel for them, which they love.
It is a smaller butterfly, but rivals the beauty of the Giant.

" they do prefer the sapote to citrus. "

Interesting since they said the sapote was originally from citrus family -- just look at the seed; very much the same except much much bigger

Sapote

It must be the taste of the leaves Sapote? I have no idea why, but they don't touch my lemons, but go nuts for the white sapote. Pic of caterpillar
(they look like bird doo) on the branch back in 2011

Here's a picture of a Giant swallowtail sitting on the snail vine (about 10 feet from sapote) from it's very first flight and subsequent landing. Sorry shot not so great, but at least people can see what they look like :)

I have yet seen a single caterpillar of any kind on my big tree. Maybe since California is an agriculture state and most pest were "fenced" off. (it's amazing to me how could they (government) even achieved this on a vast piece of land.)

Sapote

Now you made me look up their range. Here it is:
(Maybe this is why you don't see them Sapote) :)