Perennial rye is the fastest to germinate and grow, but in July those growth rates will be much reduced. Root growth is minimal in soil temps above 70 degrees, and stops around 77. Topgrowth also slows in summer, so growth rates won't be very fast regardless of the grass you plant.

Chasmanthium latifolium (Northern Sea Oats) has fabulous flowers for floral arrangements. Can be cut and used green or tan. For curiosity value the seed heads on Carex grayii would be quite good in a bouquet. Neat looking, like a tiny mace. Eragrostis spp. ~ any of the weeping love grasses have lovely airy panicles that are long lasting.

Well, you'll be limited in your choices. Virtually any taller grass, like over 2' tall, will overhang the driveway by a good deal if it is properly stood off the fence. If you plant a grass that matures to 2' in diameter, it must be at least 1' off the fence in order to mature properly. Most ornamental grasses are wider at the top than at the bottom, and a plant with a 1' diameter crown at the base could easily be 3-4' in diameter at the top. It's the diameter at the top, in bloom, that must be accounted for in both stand-off from the fence and overhang of the driveway. Even if you don't mind the grass's foliage and plumes overhanging the driveway, the strip is so narrow you'll have trouble properly installing any large grasses. That said, there are lots of small clumping grasses which will fit the space. Look at the smaller cultivars of Festuca, Sesleria, hardy varieties of Carex, like C. plantaginea, Koeleria varieties, Helichtotrichon sempervirens and Eragrostis spectabilis. For more vertical interest, maybe consider additional plantings in pots, mounted to the fence above the grasses.

My hubby has the front yard for the grass (except for two raised beds for lillies), and I get the rest of the back side of the house for my type of plants and most of them are natives as they do seem to be happy just where God planted them!I am a grass puller and a weed planter! I have such fun with what God has provided!