The offending rhizomotous plant will find the light at the opening you leave for your desireable plant. For this reason it is always best to eliminate all the exotics before starting your wildflower meadow. Remember that there are some species that can be stopped by the newspaper method, and there are others that are only set back for a time, and will reappear once the newspaper breaks down. If the plant you are protecting is a shrub or small tree, it can withstand the newspaper treatment for a time, but a more delicate meadow species may be quite resentful.
I always remind myself that it took many years to build natural meadows before we came along, and now we try to create them in a few years. Keep experimenting and look to nature for your answers by taking walks in local natural meadows. Look at the soil and the plant communities and apply what you see to your own landscape.