So, now we've finally got the full (Z) scenario (at least the main points).
On one hand it does appear to clear up some mysteries, such as why the doctor mentioned only one bullet hole, or how a stunned and badly injured Sheila could get upstairs (because she wasn't stunned and badly injured).
It also helps to explain why a cover-up was chosen - not just one huge cock-up, but three! (although you could say there were four - the failure to realise that Sheila was alive in the kitchen, the failure to cover all the stairways, the failure to realise that Sheila was alive in the bedroom, and the accidental shot).
On the other hand it's more difficult to believe that the police could have made just so many huge mistakes (although I suppose that stranger things have happened). It's also more difficult to believe that the police would think that Sheila was dead in the kitchen when there were no obvious bullet holes (even if she was lying next to a quantity of blood).