  In this article we apply background-independent renormalization group methods
to spin foam quantum gravity. It is aimed at extending and elucidating the
analysis of a companion letter, in which the existence of a fixed point in the
truncated RG flow for the model was reported. Here we repeat the analysis with
various modifications, and find that both qualitative and quantitative features
of the fixed point are robust in this setting. We also go into details about
the various approximation schemes employed in the analysis.
