From observation I feel that spraying with weedkiller only kills off
its competition and allows it to come back even stronger...as others
have said only cultivate as small a patch as you need, let grass or
other weeds grow in competition with it on paths and other unused
areas, just do the best you can to clear each bed and get on with
planting etc.... try not to let it become something you have to
beat...its been here since prehistoric times & will be here when we are
long gone you... will only lose any 'battle' you start

Mike