Unless you want a constant maintenance headache, I'd get rid of the grass before planting any type of groundcover. There really isn't any groundcover that is very effective in choking out grass, even very aggressive ones. You will just get a messy combination of groundcover with grassy weeds growing through it - likely more of a problem to maintain that you have now.

You can use a product that is a herbicide that targets grasses (monocots) only without fear of harming the shrubs and other plantings (Grass-Be-Gone is one) or just eradicate the grass by hand. Once it's gone then vinca, ajuga, pachysandra, lamium or even London Pride (Saxafraga x umbrosa or primuloides) would work. Bishop's weed, Aegopodium, is not evergreen and tends to be one of the more aggressively spreading groundcovers.