I got to wondering about "What I think John knows is possible", ignoring the extra problems of cognitive predicates and using / for the descriptor, since typefaces keep confusing LC ell with one and uc i. P /x(Bi/y(^Kjx^y)), which Is not going to convert easily, as you say.
But that is no reason to disparage cases that do convert easily.
Indeed, it makes me inclined to doubt the legitimacy of the form itself (quantifying in and all that).