When was the last time you core aerified and deep tine raked the lawn?
What you are saying is thatch is not thatch but stems of the leaf tissue that normally should be either a light green to almost yellow in appearance.
The fact that the leaf tissue is brown means the plant is not processing nutrients properly.
The finished height of cut should be at least 2" and in this heat probably at least 2.5".
I'd core aerify, heavily rake the cores and the lawn, BAG everything then correct the irrigation deficiencies.
Continue to bag ALL of the time, apply a foliar fertilizer according to a soil test and be patient as Zoysiagrass takes awhile to recover from stressors.
Nice Try = You Suck Spelled Differently