I never believed that Jeremy went outside to shoot rabbits.
I think perhaps the discussion inside was embarrassing or unpleasant for him, so he grabbed the gun and went outside on the pretence of hearing rabbits. Just needed an excuse to go outside.
Did he claim to go out before or after he ate?
You act as if there were some witness who said Jeremy did go outside with a gun. If he wanted to leave he could simply have gone outside to finish the work he left undone that Nevill ended up having to finish. For all we know he make up being in the kitchen and the conversation that he claims took place that night as well.
He claimed it was after he ate, but why would he load the magazine in the kitchen if he didn't want to be around the conversation? He could have loaded it in the office.
His claim of loading the gun was to acocunt for why his fingerprints could be on the gun/bullet casings and more importantly to suggest that Sheila had a wepaon of opportunity in front of her to grab. If the magazine were not loaded then as she loaded it Nevill could have grabbed the gun (you can't load the magazine with one hand). He even claimed he left out the bullets but botched that aspect. There were too many bullets to fit his story so that proves he staged the bullets after the murders. That means there is no reason to believe the rest of the story about leaving the gun out either.