I like your term "meadowification"! First, I'm assuming this is your own property and not a public one. Second, you need to get yourself a good reference book on native plants in your area. This will help you identify invasives and natives. Then I guess I need to ask what you have already planted. You must have done some homework already on native trees if they are already in the ground. I am also assuming they were planted densely enough to create a complete canopy on maturity so the ground plants will change as they grow.

OK, so I know that you have 1 1/2 acres involved so hand management is not out of the question. Some of your listed plants are annuals (scarlet pimpernel) so they are not really an issue. They are opportunists that spread their seed and germinate where there is some disturbed or bare ground. Some, while perennial natives, tend to be thugs (ox-eye) but again it may not be an issue with competition and increasing shade from the trees. Some are obviously noxious (poison ivy) and need irradication immediately. Painting RoundUp for poison ivy directly on the plant or very carefully spraying individual plants is recommended. Mowing will not eradicate poison ivy. You should also remove the Canadian thistle, either by repeated mowing or whacking, or with chemical means. It will eventually disappear with repeated cutting back. If you have Japanese honeysuckle you also will have a big problem. It will also need to be chopped back, then removed chemically with the same RoundUp for shrubs and poison ivy. On the blackberry, I would keep it, if only for the berries! and for food and cover for wildlife.

Most of the others are common pains-in-the-neck weeds but will become less prominent as shade encroaches. As for the grasses, there are so many native and non-natives that you really need a good guide or else be an expert to identify them all. It helps to know your soil and your conditions and maybe ask a few local farmers who deal with them all the time to help you. I personally love grasses and forbs among trees in a savanna type setting. Again, the ones that are suited for the conditions will survive.