It sounds to me like you're using the mulch as a matrix to increase the airflow and surface area to which your manure slurry is being applied. It is best to cover manure if it is not completely processed, so a layer of soil is probably a good idea.
Honestly, if you don't have pest problems, and if the top layers aren't keeping
water out, then if you still have any doubts, put on another layer. All it will do is add more biomass.
Buried mulch can act as water storage in the soil. I have in the past dug mini swales and dug organic matter in the form of slash and
wood chips down into them, and then put the topsoil back and planted into it. The soil retained
enough moisture from rains and dew that I didn't need to water anything.
One thing you need to be aware of, though, is the potential for woody mulch to cause a nitrogen deficiency in the soil as it decomposes. I think the manure slurry may already be making up for that, but be aware of the issue.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein