Alternative outlet grounding method.
I know it might not be up to NEC code BUT as I see it: If your wiring does not have a separate bare ground wire (just hot, neutral) you should be able to change your 2 prong outlets to 3 pround polorized ones and ground it by taking a short piece of solid copper ground wire and jump from the green ground screw to the neutral screw (silver) or into the back of the neutral screw if available. After all a proper ground wire goes to the same grounding/neutral bar in the main box.
As I said it would not be up to code but would this grounding serve the purpose. When you use a tester it shows the outlet properly grounded and not open ground.
Advise