I don't grow daylilies but, if their root structure is like Siberian Iris, I've dealt with a similar situation albeit about 1/3 the size. A bed neglected for several years had been invaded a wide variety of weeds including grasses, ground ivy and many other unknown plants.
The first year I removed all of those weeds which were visible and mulched with pine bark chunks. By year end many weeds, particularly the grasses were back "within" the clumps of Iris.
I dealt with this 10 x 10 area the following spring, in stages, over several evenings. I dug each clump and realized I had to divide them in order to remove the grass runners and rhizomes as well as possible. Then replanted, re-edged the bed and finally mulched.
I've read too many negative reports regarding the use of Roundup type products, even those designed to only affect grasses, to use them on or near some perennials.
