I bought a house and put some raised beds in the yard, on top of what we thought (in very early spring) was just lawn. It turns out there were irises (small purple ones, I don't know the variety) there. They now grow up through the raised bed, and are crowding out the plants I put the bed in for. I love irises, and would love to move them someplace else, but the rhizomes are down through 8" of soil in the bed, plus however far below the surface they were to start with. I've tried to dig them up, and get lots and lots of root, but the rhizomes are almost all breaking off and coming up separately in a second dig. Any chance these rooty but rhizome free irises are going to survive? Should I just give up on this project and try to kill them off completely?
Those look like Japanese iris (Iris sanguinea). They have a smaller, clumping rhizome rather than the large spreading tuberlike rhizomes of the bearded iris (Iris x germanica). They can grow a long, stemlike rhizome when planted too deep, and these stems can grow roots. The plant would then proceed to create a new rhizome crown near the new soil surface. You can remove these extended rhizomes before the become a new crown, as long as they are rooted in. Unrooted rhizomes have a lower success rate. Trim the leaves back by at least half if you transplant them that way.
You might get a stronger transplant if you can dig down and take the original rhizome crown, even without leaves. It would be a stronger foundation to start off of.
Your irises look very happy in this spot.
transplant without the rhizome?
The rhizome is the most important part of this plant. It will allow it to regrow the next year after a period of "sleep". But it is ok to transplant only a part of it if you can't dig them completely out. Here is how healthy future transplants would look like:
What is important is you wait the end of the vegetative period before you transplant them (usually end autumn). It is not necessary to dig them as deep as you found them.
Now if you see more coming the next years, propose them to neighbors, they will appreciate.