Just a thought, but the metal sheath of the Romex might be ground at the main panel. I know it is not the greatest ground in the world, but it might somewhat solve the problem. I have dealt with this two wire system in my mother's house too. When I would replace an outlet with modern 3-prong, I would run a ground wire to the metal box. Never verified it was actually a ground like I suggest you do. I just convinced myself it was. I WAS VERY YOUNG. The main panel is required to be grounded. You might check to see if there is continuity between the main panel case and the metal sheathing of the Romex exiting the main panel to see if it is indeed grounded. If the sheathing IS grounded and the outlet boxes are metal (usually in older homes), then the box should be grounded as well. I suspect it would not meet any NEC code, but it could be a rough hack solution. At least you would know that the outlet is connected to a ground (albeit not a great one). Of course, replacing the Romex with modern 3-wire NM cable is the best solution. But, it sounds like that is beyond your capabilities. Just some thoughts.