I am not a believer in Kitchen products for fungus control. Less costly of course. And...furthermore I am from far north of you--no personal experience with brown patch. It looks to me like Prostar(2 oz) and Heritage TL (use at 1 ounce per thousand sq ft) are the best fungicides for Brown Patch.
Thiophanate-methyl, and iprodione(Chipco 26019) are also good and probably available at larger garden stores.
It appears the Cleary's 3336 (thiophanate-methyl) is the least costly,
Take the advice of plant pathologists for this disease. Try to irrigate only early in the morning. Water deep and only twice per week to avoid wetting the leaves more than necessary. Disease becomes active in humid weather when nighttime temps remain above 60 degrees. Fungus resistant tall fescue cultivars are a good bet.