Jack in the Pulpit is native to most of eastern North America, as far south as Florida. Try to find plants from native stock in your area.

It needs a moist, shady site with humus rich neutral soil, ideally in a woodland. If well suited, plants will fruit with small red berries that readily self seed so you may eventually have a small colony. However, it is not an aggressive spreader.

Here is a link that might be useful: Jack in the Pulpit

Here in the Atlanta area, I think it IS considered a pretty good spreader. Those that have it find that new babies sprout pretty readily. While not "aggressive", it definitely is not shy, especially in the moist areas (along streambanks) that it seems to prefer.

I have also read it needs oak leaf mold for the seeds to germinate. I have over 100 growing under my oaks. Their seeds sprout, but I plant them, before the squirrels get them. I would not say they spread readily as it takes a seed 3-4 years to bloom.

Use the genus name Arisaema to do a search. There are lots of Asian species available but I believe most appreciate temperate climates.

Here is a link that might be useful: Arisaemas

Both A. triphyllum and A. dracontium are native to your area. They like organic rich soils and shady, moist conditions. There are a number of Asian species that probably would do well for you too such as A. ringens and A. serratum. A. ringens is not so much a "spreader", but it does tend to form clumps via offsets. These can be separted from the mother plant in the fall when the leaves die down. They will be a bit expensive in America, but they can be sourced at nurseries such as Plant Delights and Asiatica.