Use caution when pricing poultry litter. Price it on a 'cost of nutrient' basis. What might appear to be cheap fertilizer may be high if the concentration of nutrients is low. Evaluate your grazing strategy. If all your pasture grasses underneath that golden canopy of broomsedge are maintained at a height of less than 4 inches, seriously look at the reasons why and what can be done to enhance plant competition.
Fire does improve the forage quality of a pasture.
Regrowth after a burn will be higher quality than what was burned. However, continued use of fire in cool season pastures will eventually reduce the desired grasses. Broomsedge is a warm season grass and is not damaged by early spring fires. Probably not, due to the growth habit of broomsedge. By the time it gets high enough to mow it has reached the reproductive stage.