Your time line may be off somewhat. I believe when Hoover died installing Pat Grey was close to immediate, and announced, surprising Felt and no doubt many others at the Bureau, who since Calvin Coolidge days didn't take kindly to the thought of outsiders calling the shots. It was a quick done deal, that brought the Bureau's long held tradition of approving their own to a sudden close. I have no doubt many felt betrayed.
You are probably right.
But there WAS a time when naming a new director was under serious discussion, at least, and Felt was lobbying for the job. He'd do anything for it, as we have seen.