Sweet Autumn Clematis is quite pretty until it starts taking over. Some gardeners keep it under control by pruning it right after it flowers. This will keep it from producing and dropping seeds. Getting rid of it will take some work and you will need to be persistent. Cut out the tops, taking it down to the base but leaving some leaves. An herbicide sprayed on the leaves will go into the roots and help kill the plant. If using chemicals concerns you, check out this video of a clever gardener who used table salt and duct tape to kill a vine. Your best approach with Star of Bethlehem is to dig up the plants since chemicals have little impact. Be certain you don’t put the bulbs in the compost pile. That will only cause more plants and problems.
Good luck and thanks for writing!