We do not have total Lagrangian formulation in tensor mechanics, although, as the MOOSE developers say, we're happy to take pull requests to expand MOOSE and tensor mechanics. We have an incremental Lagrangian formulation in the crystal plasticity code of the tensor mechanics module (
https://github.com/idaholab/moose/blob/devel/modules/tensor_mechanics/src/materials/FiniteStrainUObasedCP.C) which may be of some help to you.
I'm not sure about the use_deformed_mesh and use_deformed_coordinates options. The use_displaced_mesh option will indeed influence which mesh is used to calculate the gradients of the shape functions; these shape functions are used to calculate the gradient of the nodal variable (displacements in tensor mechanics).
Would one of the MOOSE developers more familiar with libmesh and the mesh information available in MOOSE help answer these questions please?