We have PI growing underneath a clump of very ancient lilacs at our family cottage (they are at least 100 years old). We used a lot of roundup initially, now we can spot treat it. One of my Master Gardener friends said that the round up doesn't work unless it is actively growing. So spring is better than fall to treat it (I am always there in the fall, rarely in the spring or early summer) So if you are using a chemical, use it when it is most beneficial.
I too have used the special soaps for cutting through the PI oil. I wash me, the clothes and since we have a PI vine growing up one of the lilacs, which I saw through every year - even the saw blade. I also use the hottest water I can, because it is an oil which gets on things.
Apparently when I was a young-un, my father burned some PI at the edge of our woods - and yes, the smoke will carry the irritant, as he would tell you if he was still alive. He apparently got pretty sick from it all those decades ago ~Jan