Looking for non-invasive groundcover for low-growing roses, visible already in April-May (z6a,Great Lakes, nights are slightly above freezing). Groundcover roses die back to the ground and until new branches grow again in the spring, the ground is bare.

This is full-full sun front yard, sandy soil, covered by snow in winter and fierce sun from early spring (in good weather).

Groundcover should grow reasonably fast to fill the area, be not invasive (neighbors around),

do not compete with roses' roots (as Aegopodium Podagraria),

do not overgrow roses (like Oriental poppy, very early folliage, nice, z2-3),

and rose growing procedures (watering and fertilizing, mounding for a winter) should not suppress growth of groundcover.

Am I looking for not existing plant? ;)

Tried: woooly thyme, elphin thyme, dianthus, Irish Moss, variegated goutweed. Bulbs also, they are deadheaded by squirrels (including some daffodils).

Thank you.