Quinn Finite Total Homotopy TQFT is a TQFT that works in any dimension and that depends on the choice of a homotopy finite space $B$ (e.g. $B$ can be the classifying space of a finite group or of a finite 2-group). I will report on ongoing joint work with Tim Porter on once-extended versions of Quinn Finite total homotopy TQFT, and I will show how to compute them for the case when $B$ is the classifying space of a finite strict omega-groupoid (represented by a crossed complex).