I wish I could be on vacation April through October! Or do you mean that is when you periodically visit? If that's the case then I would be especially careful about what non-native plants you try. You won't be around much to monitor them, and worse yet, you won't be around much to eradicate them if need be.
That list in the link that syzone8aUK posted is pretty good. Anything that would be fast spreading in a wild forest would make me cringe. Changing the forest floor ecology has ramifications on all kinds of natural organisms. Birds, soil flora, animals, besides the native plants already there that you would push out. Have you thought, for instance, that such a nice permanent ground cover as you envision would likely attract rodents (compare to the native flora)? All I am saying is, be responsible for whatever you decide to do.
