May I recommend putting the straw or leaves on top of the manure? If the manure is a little "hot", excess nitrogen will be used to break the leaves down into humus, but if not, the nitrogen will go into soil. This buys you some leeway in the amount of fertility you apply.
If there is nitrogen-poor material on the soil surface, it will draw fertility from the soil until it is decomposed; nitrogen-rich materials on the surface can release ammonia and other foul-smelling substances.
I think having
chickens living above the soil, intermittently, would give you much of the same benefit you would get by applying
compost tea. It may be worthwhile scheduling the placement of
chickens in a particular area and the application of mulch to give detritovores have a chance to do their work for a few weeks, before they're scratched up and eaten. Mulching a manure-covered area with leaves
should allow the worm (etc.) population to explode, and chickens will be happy to turn over the leaves or straw once they're allowed back in that section.
"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.