As you've discovered, the poison ivy plant is opportunistic (via its long runners) and will invade / overtake an area that has ideal growing conditions. Have you considered spraying Round-up or similar at the edge and a little over onto the neighboring lot? Sort of as a preventative measure. I've found that with persistence particularly as the plants are starting to really spread like in spring that an area can be brought under control. My husband goes on Poison Ivy patrol on a regular basis and sprays Round-Up on any plants found.

How about a fence that goes a few inches into the ground. The runners if they go underground won't go that deep from what I've seen (I'm not an expert but I've seen a fair amount of the stuff). You could stop the runners and then treat anything that attempts to climb over the fencing.

One other problem you'll have is the dispersion of poison ivy seed by birds and other wildlife. You'll need to keep up with anything that seems to just "pop up".