Supposing that the visitor was not John Bellingham at all, but someone who was personating him?
That would dispose of the difficulties completely.

The strange disappearance ceases to be strange, for a personator would necessarily make off before Mr.Hurst should arrive and discover the imposture.

But if we accept this supposition, we raise two further questions: 'Who was the personator ?' and 'What was the object of the personation ?' "Now, the personator was clearly not Hurst himself, for he would have been recognised by his housemaid; he was therefore either Godfrey Bellingham or Mr.Jellicoe or some other person; and as no other person was mentioned in the newspaper reports I confined my speculations to these two.
"And, first, as to Godfrey Bellingham.

It did not appear whether he was or was not known to the housemaid, so I assumed--wrongly, as it turns out--that he was not.

Then he might have been the personator.