My experience with mature patches of poison ivy is it can be tamed, but it is not something that I was able to accomplish in one application. However it is something that can be dealt with. Smothering probably works very well, but in the cases I was dealing with application was impractical (crawling up chainlink fece, growing too near plants I wanted to keep, etc.) and other impracticalities kept me from renting goats.
Spraying with vinegar (peroxide works too, I just usually had larger quantities of vinegar on hand) can help wither the leaves (hot days make it scorch that much better, add a little soap so it stays on the leaves longer if you wish.) Boiling water will kill the roots (but is not practical in most places, using an electric kettle and extension cord allows a little more range. Decreasing shade didn't seem to knock it back any, but the ivy was less likely to re-enter an area that was made to be sunnier. Chopping the plant with a shovel or machete is good (or any mechanical means). This is especially effective for where it climbs. I usually chop it twice on the tree and knock the cut section away (I swear the two ends can mend themselves back together if close enough.) When cut on the ground I try to flip the vine away so the cut portions aren't still buried, allowing them to re-root before the wound dries out. If I had the vinegar with me while I chopped the vines I would squirt some on the wound; probably helped, but I couldn't tell enough of a difference to make it worth walking back to the house to get the vinegar if not already on hand.
I mainly used the vinegar and machete as my tools for getting rid of the ivy, the boiling water was too much of a hassle in most cases and I always worried about scorching some desired plants roots that happened to be in the same area.
Anytime you know you will be going near an area of poison ivy you want gone, carry something to cut vines with (machete, shovel, snips, hoe, anything really) and/or a bottle of vinegar (or peroxide if you have it) with you. Don't have anything with you, mulch over any poison ivy leaves you see (being an "edge" plant, there is usually some natural mulch around you can re-position). The main thing is to just stay on top of it, it's remarkable what an extra two minutes of effort each trip by can do for not allowing it to gain any ground (walking by and drop a shovel on the vine and flip the wound up as you remove the shovel from the ground, or squirting the leaves on your way to and from the garden/woods/ swimming hole). This allows you to slowly work it back and keep any ground you gain, it is especially frustrating to work on a patch for a whole afternoon eradicating it and come back later and it look more vigorous than before because you didn't get every last bit of it. out of the ground.
So, increase sunlight if possible to deter plants, knock it back mechanically and/or with vinegar/peroxide (soap allows it to stick on plant longer). Then keep it back and starve it out by killing new growth before it can provide significant food to the root system.