I believe that is nutsedge. Ortho nutsedge killer is very effective against it.

Agree. Don't waste your time pulling them up. They have very fragile root system with a bulbous, nut-like, growth down a few inches. The roots easily break off from the nut leaving the nut in the ground from which you'll get 10 more spawn. Just spot spray the ones you have and keep after it. These are sedge plants, so be sure you get the right spray. Grass or weed killers will not work. It has to be a sedge killer.

How have you been watering? Nutgrass usually grows best in soggy soil. I have gotten rid of it simply by changing to deep and infrequent watering. If you are already watering deeply and infrequently then you might have green kyllinga. Green kyllinga is another sedge that looks like nutgrass but has a different seed head. It is much less aggressive than nutgrass and lives just fine in very dry soil. It is also a sedge and must be killed with a sedge killer.

Hmm. There were a few spots that weren't getting enough water because it would need to spin close to 360 degrees but the rest of the heads are providing enough water so I just changed out the nozzle for that one to a higher gph. I have some packets of sedgehammer that I'll use on them.

Or would it be easier to dig up and sod?

Sedges are real easy to kill, I don't think a resod is warranted.