It could add another thread to the premeditated theory? (and perhaps why the scream was heard by the neighbour - less building to muffle the noise) SE wakes up around lunch time and looks out to find MS messing with the summerhouse...could he even have started removing parts of it if she was refusing to pay? (hence the dismal appearance!) SE goes out to confront him, they argue and he strangles her. (I'm sure the MSM articles made a point of the fact that the police removed what looked like a phone charging cable from the summer house in an evidence bag)
This sounds like a likely theory to me