Do you have any suggestions for controlling the spread of some too happy Japanese Anemones? I know they spread by underground roots but do they also spread via seeds? If I put down a barrier how deep should it go?
I have also experienced this in my garden, and it is not impossible to dig up Japanese anemones and either compost them or offer them to fellow gardeners (with a stern warning!). Anemone x hybrida spreads easily by roots but can be propagated from seed. It is most likely that the spreading of the plant in your garden is mainly rhizomatous (by roots). If you don’t want to dig up the occasional clump, you could try getting rid of the plant in areas where you do not want it, and then putting barriers such as plastic edging around the clumps you want to keep, although I think this requires at least as much labor as removing any unwanted anemones. Also, cut off spent flower stalks if you want to avoid seeds. However, the seedheads are flossy and ornamental in winter.
Here is general information on this plant, from Cornell University.
Here is information from Iowa State University Extension(now archived). This may give you some ideas on ways of containing the spread of the roots.