Answer: Unfortunately very few plants can outcomplete the invasive Japanese honeysuckle and poison ivy. The vines spread far and wide once established and can crowd out other native or cultivated plants. The birds also drop the seeds and help them spread that way. Both of these are persistent thugs in the landscape and in natural areas.
Mondo grass and other plantings used as ground covers would certainly not be able to overtake them, but eventually you may be able to use groundcovers to try to limit the encroachment and re-establishment of the vines. If part of your goal is to encourage wildlife you may want to look into re-establishing a natural plant community using native plants that are well suited to the growing conditions in your acreage.
First though you need to work on the vines. They are deep rooted and very vigorous plants. To achieve control requires ongoing vigilance and perseverance. You can try cutting them back to the ground and grubbing out the roots repeatedly to exhaust the root reserves. You can try cutting them down to the ground and then smothering with a layer of cardboard topped with a heavy layer of mulch; by excluding light you discourage it from re-emerging. You can also work on them with chemical controls such as glyphosate. An old fashioned but sometimes effective method is to allow goats to graze the area, although they will eat both the undesirable and the desirable vegetation both.
I would suggest you work with your county extension to develop a control plan. As you begin to control the vines you will be able to begin planting or restoring your acreage. Your county extension should also be able to help you with that or direct you to local resource people. Your plantings will be determined by the growing conditions and level of ongoing landscape maintenance you wish to perform as well as your overall design goals for the property -- and what is already established in terms of trees and shrubs. Best of luck with your project!
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