It's strange that you should say that, "[s]yntactically, the relative clause can only belong in the embedded noun phrase with 'girls' as head" in the one example, and then that the relative clause "belongs in the topmost noun phrase with 'one'" in the other example, whose syntax is essentially parallel.
The example with Ed can go both ways, as well. Syntactically, there is nothing preventing a plural verb in the relative clause (Ed is one of her colleagues who are always ready to criticize her), unless, like many, you find restrictive relative clauses modifying possessive noun phrases questionable. But there is a fix:
Ed is one of the colleagues of hers who are always ready to criticize her.
In that sentence, there does exist a set of colleagues who are always ready to criticize her. Poor woman, she has a hostile work environment.
Returning to the example with Jill, if some members still doubt whether it is syntactically possible for the relative clause to modify "one" rather than "girls," consider that "one" may be preceded by "the only," and that, if it is, the relative clause not only can modify "one" instead of "girls," but must:
Jill is the only one of the girls who is missing.
*Jill is the only one of the girls who are missing.
For the latter to be possible, an additional relative clause would be needed -- e.g.:
Jill is the only one of the girls who are missing who has phoned her parents.
Interestingly, there, the relative clauses modify different NPs. The antecedent of the first "who" is "girls." The antecedent of the second "who" is "one."