Cheryl, I have the same problem where a clump was removed to put in decorative fence panels eight years ago. I have dug and sprayed and pulled--still occasionally get pieces coming back. As long as there is a viable piece of root, eventually it will send up new sprouts. This issue is THE reason I haven't planted a tree form Crepe Myrtle, as beautiful as I think they are. The option that has been the most effective in controlling the stuff here is painting on the undiluted concentrate of Roundup Poison Ivy and Tough Brush Killer. In some places, I have been able to place protective cardboard behind larger sections to be killed and spray it on, again with the undiluted concentrate. As intertwined as it looks to be in your beds, I'd say brushing it on to the leaves will be safest for your other plants if you choose to use the product. The only other comprehensive option I know of is to dig out
everything and try to get out every piece of root. Which, speaking from experience, is a massive undertaking.
So sorry I don't have anything more positive to suggest. Hoping someone with a better experience will chime in, which will help BOTH of us.
Edited to add: I will say that being diligent in at least pulling them out does reduce the number of suckers reappearing.
