Is it syriaca that needs to be moved?

Yes, I believe it is although I haven't seen any flowers in previous years and I haven't keyed it out on vegetation yet. I see unopened flowers this year, however, so will know for sure shortly!

If they were mine, I would wait until the fall to move them. A friend had to move a bunch of them last fall and they worked very well. His were intentionally planted though (read "shallow"): I haven't a clue how deep you'll have to dig if they're coming up from rhizome below tilling level! They have stolons more than tap roots.

One year as an experiement, I dug milkweed up, barerooted them and stored them in the refrigerator in damp paper towels and wrapped in a plastic bag. In the spring, I took them out and planted them. They did very well. Another time I had a big pot filled with milkweed. I took root cuttings that time because the milkweed was dormant. It is very good at popping back. However i would wait until fall or winter to move. You can also take cuttings from the plants and then kill the ones in your garden. Penny