Sadly, you seem to miss the obvious extention that if the Senior is indeed "poorer" than Sally (whom I chose to "match" the income situation of your "Joe"), that she would be even WORSE off than I showed! Oh, and I didn't even bring up the fact that there is a "double taxation" problem ... thanks for reminding us.
Not only is the FairTax "effective" rate for low or moderate income people less than the marginal rate, so is the effective rate of the income tax lower. No matter how you spin it, those with a currently low income tax effective rate have proportionally less "money to start with" in their pockets under the FairTax. Now, you might argue that the point of the FairTax is to make low income taxpayers pay more Federal Tax. Fine. Make that argument. I might even agree that is a good thing ... but, please, don't try to handwave away the real eventualities that many would face under that FairTax.
To accept your anecdotal tactics is to accept willful misrepresentation.
I'd love to see you back that up with numbers, rather than your repeated assertions.