quince bushes and vines

Hi,
I have a growing (pun intended) problem with a vine, honeyvine milkweed, that is taking over my flowering quince bushes. The quince bushes grow in clumps which consists of a large group of shoots numbering somewhere between 50 and 75. The weed is taking over the entire row of bushes, and I am unable to find information about killing this weed. Most of the information on the internet pertains to infestations in corn fields.
The honeyvine grows incredibly fast, and the dense nature of the quince bushes make it very difficult to see where the vine is growing from. Any suggestions, thoughts, advice will be greatly appreciated.
TIA for any replies.
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