Need to see some up close shots but it Looks like the same leaf spot fungus I'm dealing with. This summer has been the rainiest summer on record. Nothing but cloudy, rainy, not super hot, and humid every day. Perfect environment for fungus.
Hopefully since it's suppose to be sunny for most of the week that might help a bit. Your lawn guy is pretty good with his advice. I don't think it will be worth it this year. We only have about 7-8 weeks left before the bermuda goes dormant. Not to mention the growth will be slowing down as the nights get cooler. By the time you go through a few rotations of fungicide, the bermuda won't be growing vigorously enough to "grow out" of the damage and look good again.