You're not misusing the word.
After the local use of "rationality" was established, a second word actually gained a meaning that is nearly as close to "rationality" (as used here) as "rationality" (as used elsewhere) is.
That word is "winning", used in the broadest and most general way, as popularized by Charlie Sheen. This doesn't imply an endorsement of any particular thing related to him, but the term "winning" did approach what is meant here by "rationality" around New Years, or whenever that media flurry occurred.
Even so, "winning" might be a bit farther from LW "rationality" than standard "rationality".
Others might disagree with my assessment.