Hi - We cannot say for sure what these weedy grasses are. At a minimum, we would need to see the flowers of the plants in full bloom in order to determine if these are seedlings of Pennisetum or Miscanthus or something else. If you do not want to use chemical methods of control (and a systemic herbicide would only be effective on actively growing plants anyway) you can either: 1) decide to leave it as is and just keep the area mowed 2) try to dig out the patches of weedy grass you do not want and overseed with grass seed to fill the bare areas 3) decide if you want to renovate the whole or part of the area -- either by smothering (or chemically managing) the weeds and then re-plant with turfgrass. It really comes down to  what you want to accomplish in this space. Some people will focus their efforts on maintaining an area of nice lawn closest to their home where it most often gets utilized, and then choose lawn alternatives (meadow, garden beds, other groundcovers) for the areas further out.
Here are our pages for information on lawn alternatives as well as lawn renovation.
https://extension.umd.edu/hgic/topics/lawn-alternatives
https://extension.umd.edu/hgic/topics/lawn-renovation-and-overseeding

Christa

Thank you  My frustration is that the grasses are definitely spreading.  I do maintain an area right around the house that could be considered a decent lawn - how do I keep this invasive from coming into that space?  Perhaps you are suggesting that I use a shallow trench to better define this section ("meadow") and limit the creep into the lawn area?  Also, if I wanted to test a little herbicide on a small area, what do you recommend that I use?  Thanks in advance.  

We have a few more questions to ask. Do you have ornamental grasses planted elsewhere is your landscape? As you mention miscanthus, cortaderia, or pennisetum can become invasive but they tend to start to invade areas close to where they are planted.
What kind of grass seed do you plant in September? Is it some type of grass seed mixture with different species of grass. This is a longshot but perhaps it has some type of annual grass in it.
We can try to id the grass again but let one of them grow taller, perhaps even develop a seed head and take the picture while it is still green.
What kind of root system does the grass have? It looks like a clumping-type grass. If you want to try an herbicide you would need a non-selective one that contains glyphosate. However, for it to work the grass would need to be green and actively growing. The dead grasses need to be dug out. 

Deb