Neither of these plants will spread uncontrollably. Most plants spend their first several years after transplanting developing their root network - then they put their energy into growing aboveground. I would transplant away. Like any plant, they may need dividing in a few years, but I would not worry about them "taking over."

The Podophyllum spreads steadily over large areas given good soil, moisture and some shade. I have areas where it covers literally 1000 square feet at a time, though I realize these plants (and root system) have been growing for many years.
I garden at the woods edge and this plant definitely spreads into cultivated areas, developing larger swaths annually. Hopefully you can tolerate that encroachment as part of your garden's style and appearance.

Rx

Rx, the podophyllum spreads, but I have found it to be fairly easily contained or removed, unlike some spreaders that are much more difficult to remove from an area. That's why I said that they wouldn't spread uncontrollably.

Podophyllum certainly won't spread far into sun, and does not like disturbance, so, if you walk around the edges of where you want it to be, it shouldn't spread.

And i think its unlilely that the seeds of Podophyllum will get to new areas, unless you have box turtles in your yard! The rhizome is what you need to worry about, but its not a big problem.

Thanks for the input. I wonder if you have any thoughts on a related matter. I've noticed there is quite a lot of white snakeroot volunteering in my yard. Any experience, good or bad, with this as a woodland garden plant?