So does the card on the body, which might have been prepared in the house.
That all fits into your hypothesis, Watson.

But now we come on the nasty, angular, uncompromising bits which won't slip into their places.
Why a cut-off shotgun of all weapons--and an American one at that?
How could they be so sure that the sound of it would not bring someone on to them?
It's a mere chance as it is that Mrs.Allen did not start out to inquire for the slamming door.

Why did your guilty couple do all this, Watson ?" "I confess that I can't explain it." "Then again, if a woman and her lover conspire to murder a husband, are they going to advertise their guilt by ostentatiously removing his wedding ring after his death?
Does that strike you as very probable, Watson ?" "No, it does not." "And once again, if the thought of leaving a bicycle concealed outside had occurred to you, would it really have seemed worth doing when the dullest detective would naturally say this is an obvious blind, as the bicycle is the first thing which the fugitive needed in order to make his escape." "I can conceive of no explanation." "And yet there should be no combination of events for which the wit of man cannot conceive an explanation.

Simply as a mental exercise, without any assertion that it is true, let me indicate a possible line of thought.

It is, I admit, mere imagination; but how often is imagination the mother of truth?
"We will suppose that there was a guilty secret, a really shameful secret in the life of this man Douglas.