Your eastern species needs full sun all day and a well draining soil. One that is probably sandy and rocky or gravelly. Check the link below to see images of plants in situ.

Here is a link that might be useful: Opuntia humifusa

One sight that I will never forget is a sheer wall of Opuntia near Petersburg WV. We were coming down the mountain from the wilderness area known as Dolly Sods. The cacti was all yellow with bloom. It was growing in shale gravel, no other plants.
I have also seen it in the sandy dunes of the Coastal Plain. In these xeric areas few other plants are growing, perhaps bayberry.
You can grow it in heavier soil but it is a constant weeding project. I guess you know that the little spines are like harpoons.

I have seen prickly pear mostly near the coast in dunes that are growing in with plants like Little bluestem, bayberry, blueberries, huckleberries, and oaks. It grows in full sun, and very well drained, sandy soils, at least in the places I have seen it.

We have some growing in the crevices of some glacial rock (or maybe on top of the rock?). I can't say if the ones we have are native or not but they survive the winters just fine. There are some acid loving shrubs close by. All of this was intentionally planted in prior generations. The location is a couple of miles inland from the east coast. I don't know whether any of this mimics natural conditions or not.

Thanks to all who responded. I can't believe it took me this long to check back--actually I was looking for something else I'd posted.

I appreciate all the feedback. You've given me a few ideas.

I did move some of it to a rock outcropping near where I'm also trying to establish lowbush blueberry and little bluestem.

I am still wondering if it is native to my area this far from the coast.

Here is a link that might be useful: A Native Backyard