I think I just found the poison ivy equivalent of the massive creature from the movie 'Alien'

[usonian]

6. I have snuffed giant poison oak vines.

There are non-Roundup weed killers that will kill them to the root. Let it soak into the leaves and down the stem.
Cut later if you do so.

Alternatively, I use a manual pole pruner (Fishers) and snip it at the base.
Snip plants often enough and they get no nourishment from the (departed) leaves and they just die.
The pole pruner is also good at grabbing the cut vine and hauling it (at a 4 or 5 feet distance from you) to a trash pile.
That's where the segments come in handy. You can't yank a vine twisted around a trunk.
Do not burn.

The oil remains even when the plant is dormant, and that's when it looks like every other dormant plant. "GOTCHA!"
That's why I haul any cuttings to a special pile, and spray in the spring when the leaves are red.

it will all take time because poison (oak|ivy) seem to have extensive root systems.