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[Tambrey]

I did not know that about wisteria!! Mostly I studied plants for our zone4, but I admire plants in other zones as well...
If you want to get rid of it, I would do similar to what they recommend for Virginia Creeper and Canadian Thistle...

wait til the killing frost (if you get them there!) and make a knick in the plant enough to get into the vascular system, but do not cut it entirely, you want the plant ton be able to continue to draw in nutrients for a while...then use a sponge brush (wear protective clothing and cheimcail gloves and goggles) and dip the sponge brush into a concentrated high strength RoundUp (I usually do not like to use any "-icides" but sometimes drastic measures are called for!) dab the RoundUp soaked sponge brush into the wound you just made on the plant, and be sure to really push the RoundUp into it good...you can also brush some of the leaves for additional application, but it needs to get into the vascular system and down to the roots fast!
do this to every plant if a grouping or several places along a vining plant, and the plant will draw the RoundUp deep into the vascular system into the roots and eventually kill it from the inside out...if you have a killing frost, it just sort of sits in the plant all winter long, and in the spring when the plant awakens again, it courses through the vascular system once again...
Alot of plants have deep roots (Canadian Thistle can get up to 18 feet deep!) so you really need to make sure it gets into the plant completely...and by doing it this way, you are being very selective and not harming anything else or leaving chemicals for animals to get in to...
RoundUp becomes immediately inert once it hits the soil and is no longer "active"...it only works on/in the plants themselves...but of course, is not good for humans and animals to get on or in them!!!

I got this information from a forrester when I was trying to get rid of the virginia creeper here!