I think I just came across a problem with the current solution.
A poor swindlecant could say, "I am not a poor honestant," because we would break the sentence down to (part A) "I am not poor." and (part B. "I am not a honestant." Since he could be a poor swindlecant, he would be lying by saying he is not poor, so we would have Part A as False and Part B as True. False and True is always False so, I don't think this would work as a poor swindlecant and a rich honestant can both say it.
Let me know if I'm wrong, or missed something.
You're breaking the sentence down incorrectly. In fact, you don't need to break it down at all. The statement "I am not a poor honestant" can only be said by a swindlecat if he IS a poor honestant, which is obviously impossible. Here's the equation you're looking for:
Does "Poor swindlecat" = "poor honestant"
No, of course it doesn't. So if a poor swindlecant says he is not a poor honestant, he is telling the truth, because the two are not equal. Swindlecants can't do this, so the sentence cannot be said by a swindlecant.