If you are struggling to 'weed' it out the best thing i find is to empty the bed of everything you want to keep and leave it empty for a season. Whilst its empty spray off the bed periodically with 'round up'( i mean a good ish one like gallup 360) and keep an eye on it. I know spraying is not to everyones tastes and someone may have a better solution but its how ive got rid of things like willow herb in the past.
Providing all looks clear after a season empty (you may want to fill it with a good suppressing green manure a couple off months before replanting, there are loads) you should be fine to put all your favorites back in.
Hope this helps, its really a last ditch effort, so with any luck somebody out there may have a better option for you.