At this point, town is playing a losing game unless we throw out extra info that will help win the game, from my point of view (other info is not relevant). Hence my claim of Emma Planck to begin with. Just going with random or inactive lynches isn't working when you're not hitting mafia to see correlations, no need to continue a losing strategy.
Maybe if literally all information was on the table, Frederica Tesla would be able to discern some Core usage. But so far, unless it was Core of Reason, there has been no visible Honkai Core usage, so there does not seem to be significant use out of that.
I really can't tell if outing all this info was the best move, but continuing the old course meant a certain town loss.