I'm not allergic either (yet!), but I treat poison ivy with respect. There was a huge vine on a fence when I moved in. I used a contractor bag to "collect" the top part, then cut it off at the base as close to the ground as I could.
I try not to use heavy duty herbicides, but there are some plants that are the "undead". For those, the ultimate killer was Bayer Advanced Brush and Stump Remover (or any herbicide with the active ingredient Triclopyr) which I painted on the "trunk" with a disposible brush within 10 minutes of cutting the plant/vine. The 10-minute limit is because the cut end of the plant immediately starts to callous. It only took 1 application.
Glypsophate (like RoundUp) is not nearly as effective. I've used the Triclopyr products when I gardened for other people and in my own garden and have never heard of or seen any translocation to nearby plants.
Technical pesticide info about Triclopyr:
http://npic.orst.edu/factsheet...
And, of course, we really all should love Toxicodendron as it's a NATIVE and according to Texas DNR, the fruit is an excellent bird and wildlife food.
