+1 on watering deeply. Deep roots are critical in summer around here.
An easy way to know how long to run the irrigation to get 1" of water - put out a tupperware container, check the time, and then run the irrigation until there is 1" of water in it. That's how long you need to run it to get 1" of water on the lawn.
Around here, most clients that have success run their irrigation 1", once a week, or 1/2" twice a week if running a whole inch at one time leads to runoff.
Like the other members, if this was turf that I managed, I would treat with the appropriate fungicide by using the NCSU website to identify the particular fungus you have, by checking the leaves etc etc. It's tough to identify without getting up close and personal. That's why I posted all three links, to show that different diseases can look the same from a photo.
If I was stumped, which happens, I would call NCSU and have one of my old profs come out and id it for me. Most land grant universities have turf experts who love to get out into the field and help out homeowners.
I would also not apply fertilizer, especially biosolids, until I got the fungus under control.
That being said, bermudagrass can certainly outgrow just about anything. I have some clients who would prefer to wait it out, and some who can't stand seeing any imperfections, especially disease, and would want me to do something, and now.
You seem like the kind of client that would want to do something, so if I was managing your turf, I would positively identify your disease and treat accordingly. Once we had that problem solved, then we could put down the appropriate fertilizer (maybe GreenTRX, or something with SOP) or even dump some milorganite on it, if that's what you wanted. I sure would want to know if you were putting down anything on top of what I was applying, however.
Hope that helps.