I don't know where you're located alsnavely, but here in the midatlantic/south east/mainland NY I've been using aggressive native volunteer plants to help me fight the fight.
don't know if this'll work for you because virginia creeper is one of the plants I encourage. :)

also (native volunteers): Impatiens capensis (jewelweed), circaea (enchanters nightshade), Viola sororia aka Viola papilionacea (common blue violet), Polygonum virginianum (virginia knotweed), Geum canadense (White Avens), Fragaria virginiana (wild strawberry), Polygonatum commutatum (solomons seal), Eurybia divaricata aka Aster divaricatus (white wood aster) to name a few.

I've encouraged these because the price was right, these are easy to pull up (or xplant elsewhere) if you have something more desirable to plant in it's place, and they benefit wildlife.

I've also planted asarum canadense (wild ginger), Eupatorium purpureum (joe pye weed), Asclepias incarnata (swamp milkweed), and Geranium maculatum (wild geranium).

the fact that these plants are aggressive (some consider weedy) is what makes 'em prime candidates for this situation.

If you have an area that you can spend more time with, and be even more diligent - maybe an area closer to the house, then I think something a bit less assertive might work.

good luck to you - and keep pullin' out those nasties

I agree that the best way to prevent Garlic Mustard from returning is to have something else grow in its place. The more aggressive natives are the best choice for this, since they spread rapidly. i think what you can expect is at first, aggressive natives will blanket the whole area, then over time, if the soil is not disturbed, the native soil microorganisms, chemistry, etc. return and more diverse natives can return or be planted. Stable areas of woodland floor take time to establish.

I like Bubble's plant list. Another aggressive native (sometimes) is Virginia Waterleaf.