I have an area in my yard that I'm hoping over the next couple of years to transform into a permaculture food forest or garden. I'm pretty new to all this so I'm hoping for some advice on how to deal with a massive amount of opportunistic Wisteria, Chinese Privet and English Ivy. They were basically left unchecked for 15-20 years (prior to my residence) in a particular spot in my yard to the point that there are Wisteria vines as big around as my fist (and I'm not a small person!) and a privet bush that had grown to be a 15ft tree and depositing hundreds of seeds (now saplings). In the areas where we beat back some of the wisteria two years ago, English Ivy has started thriving. Thankfully most of the live wisteria has been cleared from vertical growth only creeps along the ground at this point.
I would love to be able to plant a cover crop in this area this year as I continue observing and planning the entire yard but I'm not sure how thorough I need to be in removing the inground vines or which cover crop may be best.
I have cleared some very similar areas with wisteria and ivy. I would recommend chopping to the ground anywhere you don't want it, but don't get too crazy about ripping out all the roots. Ivy is already quite a nice cover crop if you keep it in check, which is easy to do. Wisteria can make some pretty features if you guide the vines and keep them in check -- the Wisteria covered bridges in Japanese gardens are beautiful! (Google some pictures if you haven't seen them..)
Find a time once a year to trim things back to acceptable areas - this will keep them from excessive spreading or choking of trees.
I had the same problem on my property last year...except w poison ivy instead of English.
We sheet mulched the plot we wanted to use after my third poison ivy outbreak.
Luckily the only thing that grew through the sheet mulch last year was a little wisteria and some blackberry weaklings, unfortunatly now I have more woodchips than places to plant. Working on learning about lasagna gardening to potentially make more and richer soil on top of the chips.
I’m sorry I don’t have a better solution. But I feel your pain.