Following the work of Asaeda and Frohman, we explore a variation of Bar-Natan skein modules which can be defined as a TQFT using Kevin Walker's fields and local relations. We prove analogous results to Asaeda and Frohman for this variation, and discuss the potential to compute skein modules of manifolds by decomposing the manifold into pieces and tensoring together the skein modules of the pieces. We give computations toward that end, and on the way give an application of the cyclic seiving phenomenon.