Ornamec is a grass herbicide that can generally be used around groundcovers, shrubs and trees. Check the label to make sure it is safe to use on your creeping phlox, and make sure to follow all label directions.
I learned from my local landscaping contractor that the reason for lots of that crabgrass roots are to blame. When the garden bed is connected to the lawn the shoots of the root system simply grow sideways into the planting bed. To counter act this they suggest that you take a shovel and dig a v shape grove down to below the root level of the grass itself. Keeping this with the vertical cut along the grass with the other cut leaning into the garden. This cut creates a air gap of sorts that prevents the roots from traveling into the planting bed, Once you weed out the remaining offending crab grasses you should see this issue coming under control. Another benefit of this is that any mulch cover will not run out into the lawn when it rains hard. It catches the mulch in the cut out. Once the rain stops you simply rake the mulch back into the garden.
make a note on your calendar to apply Preen weed preventer to the bed next spring