The grass that has invaded your flowerbed is probably quackgrass, not crabgrass. Crabgrass is an annual grass that dies out at the end of the growing season. Quackgrass spreads by underground rhizomes and is a perennial.
The techniques you've described should eliminate the quackgrass in the bed. However, any little piece of the rhizome that remains in the soil can resprout and start a new plant.
You could also put a vertical barrier of landscape fabric at the edge of the bed to help prevent the rhizomes from creeping into the bed from outside. It also pays to watch closely for new sprouts of grass, and remove them as soon as you see them appear.