In explaining the paradox, a potential analysis is assumed to be a relation between concepts rather than the verbal expressions used to illustrate them.
If the verbal expression is part of the analysis, then we shouldn't expect complete intersubstitutivity even in cases of correct analyses.
However, this response seems to move the notion of analysis into mere linguistic definition, rather than doing interesting work with concepts.
Another response is to bite the bullet and just say that correct analyses are uninformative — which then raises the question of what positive cognitive notion should be used instead of this one, if any.
One further response would be to take Willard Van Orman Quine's position and reject the notion of conceptual analysis altogether.