How is burning it gonna make it worse?

Like I said earlier, I have plenty of experience treating it in normal situations like you just mentioned.
This application is under different circumstances.

Burning is the only way you will have green leaf area to spray before it flowers out. I'm pretty sure someone with your background is well aware that it burns hot. Thinking outside of the box may provide you with a really effective treatment. I commend your efforts; I wish more down my way would have tried to be aggressive in treating this stuff. You may have a chance in your area, but it is nearly a lost cause not too far south of you Okatuppa

From the Alabama Coop Extension Sys:

Cogongrass benefits from fire. The rhizomes (underground stems) resprout very quickly and aggressively following a fire (figure 2) and often come in more densely than before the fire. Flowering is promoted by winter fires (figures 3 and 4), and the seed, which needs mineral soil to germinate, can establish more easily on ground cleared by fire.

That said, if you burn it, and then treat it after it gets about 10-12 inches and before it flowers, burning can help, but most people can't time that just right.