Northeast Gardening: What perennials can compete with a tree's root system?, 0 by jablum

jablum wrote:
There is a section of my yard, under the spread of a large Swamp Maple, where the tree's dense, matte-like roots extend toward the surface, thus consuming most of the moisture and air. The tree's canopy is high so the area receives full sun. I have a sprinkler system there so lack of water is not the main problem.

If you look closely at the picture, you can see that the grass dries out the closer you get to the tree. Along the horizontal section of the fence, I've planted Double Knock-Out roses. The three nearest the tree are barren, followed on the right by a partial bloomer, and to the right of it a full bloomer.

Along the vertical section of the fence, I've planted Paeonia lactiflora 'Karl Rosenfield', which are in their second year. While none have bloomed yet, the two nearest the tree are stunted.

I’m thinking about replacing the three roses and three peonies closest to the tree with something that will thrive under those conditions. What perennials can compete with the tree’s root system? I would prefer a colorful rebloomer. Could Coneflower compete?