The free energy change that you quote for the phosphoglycerate kinase (PGK) forward reaction is, of course, the standard free energy change (ΔG0') for the overall reaction. The standard free energy change is defined for all reactants at a concentration of 1M. Note that this value includes the formation of ATP - the free energy of hydrolysis of 1,3-BPG would be much larger, and some of that energy is 'captured' in the ATP product.
The actual free energy change for the PGK reaction, ΔG, will differ from this value because of the fact that the actual reactant concentrations are very far from the idealised 1M. You can find a Table here which compares, for each step in glycolysis, the standard free energy change with a true free energy change, calculated on the basis of cellular conditions in erythrocytes (also shown). You will see that for the PGK step the actual free energy change is 0.09 kJ mol-1 rather than the -18.9 kJ mol-1 that you quote in your question.
You can also see from the Table that there are only two reactions in the glycolytic pathway with large negative values for ΔG: those catalysed by phosphofructokinase and by pyruvate kinase. These are of course the two steps that are bypassed in gluconeogenesis because they are essentially irreversible.
So - your reasoning was correct, but it was based on the wrong ΔG values.