As noted above, baking soda is not a neutralizing solution here. Dilution with water remains your best option. Consider that when using it as actual oven cleaner, rinsing the sponge used to wipe internal oven surfaces with water in the kitchen sink would be a normal procedure. When you're ready to season them, washing with dish soap (preferably Dawn), rinsing, and drying well will be all that's necessary.
The remaining spots on the outside of the pan will probably not be affected by further treatment. Build up with no grease left in it has nothing for the lye to act upon. Your S/S scrubber is the best choice there.