A quick google search showed that both of the plants you listed have potential toxicity to livestock.
To make sheet mulching work, you need to provide materials that the plants you are trying to smother cannot grow through. To smother simple grass it doesn't take much but to smother out an perennial with a strong root system you are going to need a more than newspaper, cardboard is used for a reason. I have an infestation of nutgrass I am trying to smother out and two layers of cardboard are sometimes not enough.
Google the plants and find out when the best time to mow them is, most plants are the most vulnerable when they first emerge or right after they flower. That works far better on annuals than perennials where going after the roots are a much more effective, if far more labor intensive, solution.
Another thing to keep in mind is that a barrier like cardboard is easier for roots to penetrate downward than for a plant to grow up through. Another trick is to lay down the cardboard and enough fine mulch/compost/soil for a cover crop to grow. Again, easier said than done as that is a lot of labor and
compost but it is very effective in choking out annuals.
Just planting a cover crop isn't going to do much unless you know when your "weeds" grow and when your cover crop grows as you need your cover crop to grow fast enough to shade out the weeds, weeds will win that almost every time. Its not simply a matter of throwing down rye or clover seeds and you are done.