It is known that within the interacting electron model Hamiltonian for the one-dimensional 1/4-filled band, the singlet ground state is a Wigner crystal only if the nearest neighbor electron-electron repulsion is larger than a critical value. We show that this critical nearest neighbor Coulomb interaction is different for each spin subspace, with the critical value decreasing with increasing spin. As a consequence, with the lowering of temperature, there can occur a transition from a Wigner crystal charge-ordered state to a spin-Peierls state that is a Bond-Charge-Density Wave with charge occupancies different from the Wigner crystal. This transition is possible because spin excitations from the spin-Peierls state in the 1/4-filled band are necessarily accompanied by changes in site charge densities. We apply our theory to the 1/4-filled band quasi-one-dimensional organic charge-transfer solids in general and to 2:1 tetramethyltetrathiafulvalene (TMTTF) and tetramethyltetraselenafulvalene (TMTSF) cationic salts in particular. We believe that many recent experiments strongly indicate the Wigner crystal to Bond-Charge-Density Wave transition in several members of the TMTTF family. We explain the occurrence of two different antiferromagnetic phases but a single spin-Peierls state in the generic phase diagram for the 2:1 cationic solids. The antiferromagnetic phases can have either the Wigner crystal or the Bond-Charge-Spin-Density Wave charge occupancies. The spin-Peierls state is always a Bond-Charge-Density Wave.