Recently, equivariant Floer homology has been used to construct a number of spectral sequences between Floer-type invariants of 3-manifolds and knots. We will discuss an alternate formulation of equivariant Lagrangian intersection Floer homology, with applications to invariance and computability of these spectral sequences. This is joint work in progress with Kristen Hendricks and Sucharit Sarkar, and is partly inspired by work of Paul Seidel's and a question of Tye Lidman’s.