These methods to calculate free energies require that configurations of the unperturbed sample sufficiently well those of the perturbed system. Creating a charged ion in water is a huge perturbation to the solvation environment, causing many water molecules to reorient. You should proceed by quite small steps, activating the ion-water interactions (LJ, Coulomb) gradually. At each equilibrated trajectory, you can calculate a using FEP or BAR the free energy changes resulting from small variations in lambda.
That’s what the compute fep is meant to do, combined with fix adapt/fep to change the parameters stepwise during one long trajectory from the initial to final state, with equilibrated stages at each value of lambda.
What you are doing using the rerun command is similar to Widom test particle insertion, which only works for small non-polar solutes in solvents, that will find spontaneous cavities with sufficient size and will not induce reorganisation of the solvent. It will not lead to meaningful results for large or charged solutes.
You can learn about the technical issues with charged species from:
- Hansen, N.; van Gunsteren, W. F. Practical Aspects of Free-Energy Calculations: A Review. J. Chem. Theory Comput. 2014, 10 (7), 2632–2647.
- Hünenberger, P. H.; McCammon, J. A. Ewald Artifacts in Computer Simulations of Ionic Solvation and Ion–Ion Interaction: A Continuum Electrostatics Study. J. Chem. Phys. 1999, 110 (4), 1856–1872.
- Hummer, G.; Pratt, L. R.; García, A. E. Free Energy of Ionic Hydration. J. Phys. Chem. 1996, 100 (4), 1206–1215.