Question
James, my question is two fold. Can i spray liquified sheetrock over the lawn, and can I make a compost tea with microbrewery renderings to followup spray with and render the clay soil more fescue friendly?

Answer
Hi Mike, I would not apply sheetrock to a lawn.  If you need to adjust your pH, use lime.  In heavy clay soils, gypsum slows water movement and can cause drainage problems.  We use it to seal leaky ponds.  The best and quickest way to improve your soil is to till it and mix organic matter into it.
Your renderings would feed your soil microbes and improve your soil, but I'd try it on a small area first. Harmful fungi may also like your mixture and you might not have the effect you want.  Jim