who/whom special case with "say"

I run across cases like this all the time and I keep going back and forth.

"[The director], who [producers] [say] [is a great collaborator], got his start in television."

Reverse it and you might be inclined to say whom:

Whom did the producers say is a great collaborator?

The producers say the director is a great collaborator.

But I don't think that's correct, because the object in the above sentence isn't "the director" but "the director is a great collaborator"

The producers [subject] say [transitive verb] the director is a great collaborator [object]

It should be "who" because "is" is intransitive, and the subject of "is" is "the director"

The director is a great collaborator, producers say.

Another way to do it is to cut out "producers say"

"The director, who is a great collaborator, got his start in television."

I don't know if this comes up with any verb other than "say," but boy does it throw me for a loop. I hope someone here can give me a good explanation as to which I should use.