In this article from 1990, Stover describes a specral sequence which converges to the higher homotopy groups of the homotopy colimit of a diagram $\underline{X}$ of topological spaces.
The second page terms $E^2_{p,*}$ are described as values of the $p^{th}$ derived functor of the colimit functor $\lim_p (\pi_*(\underline{X}))$ (where I use $\lim$ to mean the colimit functor) on the associated diagram of homotopy algebras $\pi_*(\underline{X})$. Here, for $p=0$ we take the normal colimit functor $\lim (\pi_*(\underline{X}))$.
This derived functor is defined as $\pi_p({\lim{F_*}})$ - that is, the $p^{th}$ homotopy group of the simplicial $\Pi$-algebra $\lim{F_*}$, where $F_*$ is a free simplicial resolution of the diagram $\pi_*(\underline{X})$.
In order to take the above $p^{th}$ homotopy group $\pi_p(\lim F_*)$, we need the face and degeneracy maps in the simplicial object $\lim F_*$. How are the face and degeneracy maps for $\lim F_*$ defined here?
More generally, are there examples in the literature of the usage of this spectral sequence in making concrete computations - or alternatively in aiding computations?
EDIT: Having offered a bounty on this question which has since expired, I would like to emphasise that a satisfactory answer would be one which answers my question about the face and degeneracy maps. An answer to the second, more general question, would be a bonus.
