I think my only hope to get rid of this particular patch of poison ivy will be to snip the vines and apply Tordon RTU to the stumps.
Some of the vines are 1”+ thick, and are grown up into a huge multiflora rose bush and some wild plum and persimmon trees.
It’s a seriously bad patch of poison ivy.
Good luck! Make certain you wear a hazmat suit! Do not burn them either! (I guess dry until dead and send to the local landfill!)