No, please do not mention anything about Parmenides to Elayne, she will be upset and we will confront and some other troubles. Parmenides was the great fiesta of idealists Plato and Socrates.
Sounds like all of us, and not just Elayne would line up against Parmenides. The trick would be articulating exactly WHY and WhERE we think he went wrong.
Tentatively I would say that we should apply the same analysis - that it is not Paermenides use of logic in general, but his specific application of logic and reasoning to the problem, in that he failed to ground his initial premises sufficiently in the observation of the senses, and to tie the steps in his chain or reasoning to reality verifiable through the senses.
But since I've yet to really figure out Parmenides' chain of reasoning , or his conclusions either, I can't say even that with confidence. If one of his conclusions was "motion is impossible" then we can attack that with confidence, but I can't get a fix on what his other conclusions were all about.