The roundup won't hurt my azaleas, BP?
round up will kill them azaleas deader than a road dwelling dillo.
Let the vines grow, several feet longer than the azaleas, while trying to guide them to grow from one area of the bush. Then cover the azelea with a plastic bag on a windless night and lay the vines on top. Wear rubber gloves and use a kitchen sponge to apply concentrated glyo 41% directly to the leaves of the vines. Do not spray on as you risk getting some on the azeleas even with them covered. Let the vines dry overnight and in the sun the next day for a couple of hours. Then wrap the vines in plastic and remove the plastic from the azeleas so you do not burn them in the sun. Leave the bagged plastic vines intact for a few days then prune them back like normal.
Glyo works on the roots of the plant. With any luck, and with a large enough amount of leaves treated on the vine, you will kill the root system of the vine.