I must have the wimpiest LOV on earth. I hear this story of aggressive LOV. I have a little patches all over that has gone no where for years.
That said.... in my shade garden the hostas, ferns, and other shade plants when they grow they are covered.
My other go to plants to cover are deciduous bushes, daylilies.
Really I use hostas a lot even in my sun gardens.
Here is an example of a sun garden that I have some of the LOV. There is a fairy rose bush, tansy, Coral Bells, geranium, and Hosta.