That is a hilarious request! We see it every year, too. The only grass that comes close is St Augustine and not Floratam. If that is all the damage your dog has done, then St Aug should work. It will need deep water once per week as will ANY grass you put in. The difference with St Aug is that it's the only southern grass which will tolerate any shade. And it will tolerate a lot more than you have. Chances are you already have St Aug back there. If that's the case you can nurse that until it spreads to cover the entire area. All it needs is weekly water and mowing at the highest setting. You can mow once per week or once every 2 or 3 weeks. If you want it to fill fast, then I would fertilize with an organic fertilizer once per month. I like alfalfa pellets at 20 pounds per 1,000 square feet as a fertilizer. Get it in 50-pound bags at your local feed store - sold as rabbit chow. Apply by hand for that small area. Water deeply once per week. Deep means a full inch as measured by several cat food or tuna cans set out in the yard. For that area I would use an oscillator sprinkler. It might take many hours to fill the cans, so don't be surprised. Don't look now but your dog photobombed your picture.

The suggestions you posted, Laurus Nobilis and Prunus Caroliniana, Olea 'Swan Hill' , are all very good ones. I have the Laurus and and the Carolina Laurel Cherry in my back yard. The Laurus is slow growing and seems tough. It is about 20 years old and has never needed any attention. The Laural Cherry is about 25 feet tall. It's natural habit is a very large shrub type screen. It screens my back neighbor perfectly. It's needed extremely low maintenance and has been very drought tolerant. If you decide on the Laurel Cherry be sure to get the tree type, because there are also smaller shrub sizes. Mine grew impressively fast. I almost planted Swann Hill. Several of my neighbors have. I think they are beautiful, though not a very good screen. They can get large.

Here is a close up. Bambusa ventricosa clone x is a cultivar of ventricosa and tuldoides. It is an open clumper at first, but new shoots from unspent rhizome buds from inside the clump send up new shoots between them and the young canes on the outside, thereby forming a tighter clump. It can be difficult, at times, to tell the difference between the standard ventricosa and clone x, but here's how I do it. The golden rule to ventricosa is that a buddha cane will form at some point. At least one. Also, ventricosa canes only get to about 2 inches thick here. They both exhibit the ivory bands below and above each node. They both have smallish leaves, however the clone x has very long limbs, longer than the ventricosa, and you are right the ventricosa clumps tightly from the beginning. So if the clump has younger culms on the outside like the one pictured, it's clone x. This is a pic from one of the eight sister clumps to the first picture I posted.

If OP is in the PNW and nightmare scenario described in the one response was in the deep South ("pecan trees") or similar summer climate results with hot climate bamboos like Phyllostachys will be liable to be quite different. Not only is it comparatively cool in summer here we do not get buckets of rain during the growing season, unlike much of the eastern half of North America. And all the prevalent large-growing species of maples are quite dominating, with growing of other plants beneath them (once the maples are of some size) being much more limited than with more favorable garden overstory trees such as oaks. Even here in its native region it is typical for there to be openings beneath the canopies of bigleaf maple trees, these spaces often being occupied by colonies of sword ferns as many other kinds of native plants cannot do well enough beneath them to maintain much of a consistent presence. Even comparatively small specimens of Norway Maple in local plantings often have bare soil or mulch beneath them. If you can provide adequate moisture and fertility just about all kinds of hardy bamboos will grow in substantial shade. If your site is heavily dominated by the maples the competition from their roots for moisture and nutrients will be more important than the shade from their leaves. If the trees are comparatively low-branching shorter-growing bamboos like Sasa sp. will fit with them better than taller, pointy ones like Phyllostachys sp. If you are in the PNW all are liable to become infested with bamboo mites, which seem to have become almost ubiquitous here. These make the leaves blotched- and striped-looking, can be quite a spoiler - you might want to find out more about this before investing much in bamboos. Control requires repeated applications of suitable chemicals at the right times, pretty much forever (re-infestation by new mites coming in from outside can probably be expected) - same as with growing perfect hybrid rose bushes.