Originally Posted by clawsondude
I would personally consider hiring someone to deal with it. I remember reading a newspaper article about a guy in my area who removed poison ivy from backyards. His rates seemed pretty reasonable for a chore that most would rather not do. Paying someone to take care of an acre might not be too bad. I DIY most things, but this is exactly the type of unpleasant task I might consider outsourcing.
I had a young man about 4 years ago help me in the yard with yard work and to get rid of the poison ivy I had going up some of my trees. He said he wasn't allergic to it, and I verified it was ok with his Mother. He pulled the vines off the trees without incident. I found him just by putting an add on CL. There was actually quite a few people who responded.
This, of course, is a much larger area the OP has and would probably be easier to get it ripped out with heavy machinery, or the goats. I have a 3/4 acre lot and I can't imagine trying to do an area like that by removing it personally.